Géométrie nodale et valeurs propres de l’opérateur de Laplace et du p-laplacien

La présente thèse porte sur différentes questions émanant de la géométrie spectrale. Ce domaine des mathématiques fondamentales a pour objet d'établir des liens entre la géométrie et le spectre d'une variété riemannienne. Le spectre d'une variété compacte fermée M munie d'une métrique riemannienne $g$ associée à l'opérateur de Laplace-Beltrami est une suite de nombres non négatifs croissante qui tend vers l’infini. La racine carrée de ces derniers représente une fréquence de vibration de la variété. Cette thèse présente quatre articles touchant divers aspects de la géométrie spectrale. Le premier article, présenté au Chapitre 1 et intitulé « Superlevel sets and nodal extrema of Laplace eigenfunctions », porte sur la géométrie nodale d'opérateurs elliptiques. L’objectif de mes travaux a été de généraliser un résultat de L. Polterovich et de M. Sodin qui établit une borne sur la distribution des extrema nodaux sur une surface riemannienne pour une assez vaste classe de fonctions, incluant, entre autres, les fonctions propres associées à l'opérateur de Laplace-Beltrami. La preuve fournie par ces auteurs n'étant valable que pour les surfaces riemanniennes, je prouve dans ce chapitre une approche indépendante pour les fonctions propres de l’opérateur de Laplace-Beltrami dans le cas des variétés riemanniennes de dimension arbitraire. Les deuxième et troisième articles traitent d'un autre opérateur elliptique, le p-laplacien. Sa particularité réside dans le fait qu'il est non linéaire. Au Chapitre 2, l'article « Principal frequency of the p-laplacian and the inradius of Euclidean domains » se penche sur l'étude de bornes inférieures sur la première valeur propre du problème de Dirichlet du p-laplacien en termes du rayon inscrit d’un domaine euclidien. Plus particulièrement, je prouve que, si p est supérieur à la dimension du domaine, il est possible d'établir une borne inférieure sans aucune hypothèse sur la topologie de ce dernier. L'étude de telles bornes a fait l'objet de nombreux articles par des chercheurs connus, tels que W. K. Haymann, E. Lieb, R. Banuelos et T. Carroll, principalement pour le cas de l'opérateur de Laplace. L'adaptation de ce type de bornes au cas du p-laplacien est abordée dans mon troisième article, « Bounds on the Principal Frequency of the p-Laplacian », présenté au Chapitre 3 de cet ouvrage. Mon quatrième article, « Wolf-Keller theorem for Neumann Eigenvalues », est le fruit d'une collaboration avec Guillaume Roy-Fortin. Le thème central de ce travail gravite autour de l'optimisation de formes dans le contexte du problème aux valeurs limites de Neumann. Le résultat principal de cet article est que les valeurs propres de Neumann ne sont pas toujours maximisées par l'union disjointe de disques arbitraires pour les domaines planaires d'aire fixée. Le tout est présenté au Chapitre 4 de cette thèse.

Polyphenol Extraction Optimisation From Ceylon Gooseberry (dovyalis Hebecarpa) Pulp.

Originally from Asia, Dovyalis hebecarpa is a dark purple/red exotic berry now also produced in Brazil. However, no reports were found in the literature about phenolic extraction or characterisation of this berry. In this study we evaluate the extraction optimisation of anthocyanins and total phenolics in D. hebecarpa berries aiming at the development of a simple and mild analytical technique. Multivariate analysis was used to optimise the extraction variables (ethanol:water:acetone solvent proportions, times, and acid concentrations) at different levels. Acetone/water (20/80 v/v) gave the highest anthocyanin extraction yield, but pure water and different proportions of acetone/water or acetone/ethanol/water (with >50% of water) were also effective. Neither acid concentration nor time had a significant effect on extraction efficiency allowing to fix the recommended parameters at the lowest values tested (0.35% formic acid v/v, and 17.6 min). Under optimised conditions, extraction efficiencies were increased by 31.5% and 11% for anthocyanin and total phenolics, respectively as compared to traditional methods that use more solvent and time. Thus, the optimised methodology increased yields being less hazardous and time consuming than traditional methods. Finally, freeze-dried D. hebecarpa showed high content of target phytochemicals (319 mg/100g and 1,421 mg/100g of total anthocyanin and total phenolic content, respectively).

Optimisation of environmental gas cleaning routes for solid wastes cogeneration systems - Part I - Analysis of waste incineration steam cycle

Research of advanced technologies for energy generation contemplates a series of alternatives that are introduced both in the investigation of new energy sources and in the improvement and/or development of new components and systems. Even though significant reductions are observed in the amount of emissions, the proposed alternatives require the use of exhaust gases cleaning systems. The results of environmental analyses based on two configurations proposed for urban waste incineration are presented in this paper; the annexation of integer (Boolean) variables to the environomic model makes it possible to define the best gas cleaning routes based on exergetic cost minimisation criteria. In this first part, the results for steam cogeneration system analysis associated with the incineration of municipal solid wastes (MSW) is presented. (c) 2007 Elsevier Ltd. All rights reserved.

Optimisation of environmental gas cleaning routes for solid wastes cogeneration systems. Part II - Analysis of waste incineration combined gas/steam cycle

In the first paper of this paper (Part I), conditions were presented for the gas cleaning technological route for environomic optimisation of a cogeneration system based in a thermal cycle with municipal solid waste incineration. In this second part, an environomic analysis is presented of a cogeneration system comprising a combined cycle composed of a gas cycle burning natural gas with a heat recovery steam generator with no supplementary burning and a steam cycle burning municipal solid wastes (MSW) to which will be added a pure back pressure steam turbine (another one) of pure condensation. This analysis aims to select, concerning some scenarios, the best atmospheric pollutant emission control routes (rc) according to the investment cost minimisation, operation and social damage criteria. In this study, a comparison is also performed with the results obtained in the Case Study presented in Part I. (c) 2007 Elsevier Ltd. All rights reserved.

Sensory evaluation and physicochemical optimisation of soy-based desserts using response surface methodology

The objective of this study was to develop a dessert that contains soy protein (SP) (1%, 2%, 3%) and guava juice (GJ) (22%, 27%, 32%) using Response Surface Methodology (RSM) as the optimisation technique. Water activity, physical stability, colour, acidity, pH, iron, and carotenoid contents were analysed. Affective tests were performed to determine the degree of liking of colour, creaminess, and acceptability. The results showed that GJ increased the values of redness, hue angle, chromaticity, acidity, and carotenoid content, while SP reduced water activity. Optimisation suggested a dessert containing 32% GJ and 1.17% SP as the best proportion of these components. This sample was considered a source of fibres, ascorbic acid, copper, and iron and garnered scores above the level of `slightly liked` for sensory attributes. Moreover, RSM was shown to be an adequate approach for modelling the physicochemical parameters and the degree of liking of creaminess of desserts. (C) 2010 Elsevier Ltd. All rights reserved.

Robust parameter settings of evolutionary algorithms for the optimisation of agricultural systems models

Numerical optimisation methods are being more commonly applied to agricultural systems models, to identify the most profitable management strategies. The available optimisation algorithms are reviewed and compared, with literature and our studies identifying evolutionary algorithms (including genetic algorithms) as superior in this regard to simulated annealing, tabu search, hill-climbing, and direct-search methods. Results of a complex beef property optimisation, using a real-value genetic algorithm, are presented. The relative contributions of the range of operational options and parameters of this method are discussed, and general recommendations listed to assist practitioners applying evolutionary algorithms to the solution of agricultural systems. (C) 2001 Elsevier Science Ltd. All rights reserved.

Sludge population optimisation: a new dimension for the control of biological wastewater treatment systems

The activated sludge comprises a complex microbiological community. The structure (what types of microorganisms are present) and function (what can the organisms do and at what rates) of this community are determined by external physico -chemical features and by the influent to the sewage treatment plant. The external features we can manipulate but rarely the influent. Conventional control and operational strategies optimise activated sludge processes more as a chemical system than as a biological one. While optimising the process in a short time period, these strategies may deteriorate the long-term performance of the process due to their potentially adverse impact on the microbial properties. Through briefly reviewing the evidence available in the literature that plant design and operation affect both the structure and function of the microbial community in activated sludge, we propose to add sludge population optimisation as a new dimension to the control of biological wastewater treatment systems. We stress that optimising the microbial community structure and property should be an explicit aim for the design and operation of a treatment plant. The major limitations to sludge population optimisation revolve around inadequate microbiological data, specifically community structure, function and kinetic data. However, molecular microbiological methods that strive to provide that data are being developed rapidly. The combination of these methods with the conventional approaches for kinetic study is briefly discussed. The most pressing research questions pertaining to sludge population optimisation are outlined. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analysis of polycyclic aromatic hydrocarbons in fish: optimisation and validation of microwave-assisted extraction

An accurate and sensitive method for determination of 18 polycyclic aromatic hydrocarbons (PAHs) (16 PAHs considered by USEPA as priority pollutants, dibenzo[a,l]pyrene and benzo[j]fluoranthene) in fish samples was validated. Analysis was performed by microwave-assisted extraction and liquid chromatography with photodiode array and fluorescence detection. Response surface methodology was used to find the optimal extraction parameters. Validation of the overall methodology was performed by spiking assays at four levels and using SRM 2977. Quantification limits ranging from 0.15–27.16 ng/g wet weight were obtained. The established method was applied in edible tissues of three commonly consumed and commercially valuable fish species (sardine, chub mackerel and horse mackerel) originated from Atlantic Ocean. Variable levels of naphthalene (1.03–2.95 ng/g wet weight), fluorene (0.34–1.09 ng/g wet weight) and phenanthrene (0.34–3.54 ng/g wet weight) were detected in the analysed samples. None of the samples contained detectable amounts of benzo[a]pyrene, the marker used for evaluating the occurrence and carcinogenic effects of PAHs in food.

OPTIMAX 2014 - Radiation dose and image quality optimisation in medical imaging

Medical imaging is a powerful diagnostic tool. Consequently, the number of medical images taken has increased vastly over the past few decades. The most common medical imaging techniques use X-radiation as the primary investigative tool. The main limitation of using X-radiation is associated with the risk of developing cancers. Alongside this, technology has advanced and more centres now use CT scanners; these can incur significant radiation burdens compared with traditional X-ray imaging systems. The net effect is that the population radiation burden is rising steadily. Risk arising from X-radiation for diagnostic medical purposes needs minimising and one way to achieve this is through reducing radiation dose whilst optimising image quality. All ages are affected by risk from X-radiation however the increasing population age highlights the elderly as a new group that may require consideration. Of greatest concern are paediatric patients: firstly they are more sensitive to radiation; secondly their younger age means that the potential detriment to this group is greater. Containment of radiation exposure falls to a number of professionals within medical fields, from those who request imaging to those who produce the image. These staff are supported in their radiation protection role by engineers, physicists and technicians. It is important to realise that radiation protection is currently a major European focus of interest and minimum competence levels in radiation protection for radiographers have been defined through the integrated activities of the EU consortium called MEDRAPET. The outcomes of this project have been used by the European Federation of Radiographer Societies to describe the European Qualifications Framework levels for radiographers in radiation protection. Though variations exist between European countries radiographers and nuclear medicine technologists are normally the professional groups who are responsible for exposing screening populations and patients to X-radiation. As part of their training they learn fundamental principles of radiation protection and theoretical and practical approaches to dose minimisation. However dose minimisation is complex – it is not simply about reducing X-radiation without taking into account major contextual factors. These factors relate to the real world of clinical imaging and include the need to measure clinical image quality and lesion visibility when applying X-radiation dose reduction strategies. This requires the use of validated psychological and physics techniques to measure clinical image quality and lesion perceptibility.

Les acanthopleurocératinés portugais et leurs relations avec les formes subboréales

The evolution of the Portuguese Acanthopleuroceratinae is similar to the celto-souabe succession such as it was described in the collects of the Cottards (Cher, France). A subspecies of one of the oldest Acanthopleuroceras (A. carinatum atlanticum) is abundant in the lower part of the Portuguese Ibex zone; this form is described here. The species is recognized in France by several nuclei associated with A. arietiforme (Cottards-22). Generally the similarity between the successive French and Portuguese populations (A. maugenesti, A. valdani, A. alisiense, junior synonym of A. lepidum TUTCHER and TRUEMAN, 1925), is very good. This fact suggests their specific identity. It is typical for A. lepidum of which the greatest populations allow the biometric comparaisons. In Portugal, the mesogean Tropidaceras are missing. This absence of the subboreal Acanthopleuroceras ancestors suggests the straight celto-souabe derivation of the Portuguese Acanthopleuroceras and not a similar local evolution. A. lepidum the last Acanthopleuroceras reaches the western coast of Canada (British Columbia) probably by the Arctic ocean.

An approach for reliability-based robust design optimisation of angle-ply composites

Variations of manufacturing process parameters and environmental aspects may affect the quality and performance of composite materials, which consequently affects their structural behaviour. Reliability-based design optimisation (RBDO) and robust design optimisation (RDO) searches for safe structural systems with minimal variability of response when subjected to uncertainties in material design parameters. An approach that simultaneously considers reliability and robustness is proposed in this paper. Depending on a given reliability index imposed on composite structures, a trade-off is established between the performance targets and robustness. Robustness is expressed in terms of the coefficient of variation of the constrained structural response weighted by its nominal value. The Pareto normed front is built and the nearest point to the origin is estimated as the best solution of the bi-objective optimisation problem.

Optimisation of exposure parameters for spinal curvature measurements in paediatric radiography

This review aims to identify strategies to optimise radiography practice using digital technologies, for full spine studies on paediatrics focusing particularly on methods used to diagnose and measure severity of spinal curvatures. The literature search was performed on different databases (PubMed, Google Scholar and ScienceDirect) and relevant websites (e.g., American College of Radiology and International Commission on Radiological Protection) to identify guidelines and recent studies focused on dose optimisation in paediatrics using digital technologies. Plain radiography was identified as the most accurate method. The American College of Radiology (ACR) and European Commission (EC) provided two guidelines that were identified as the most relevant to the subject. The ACR guidelines were updated in 2014; however these guidelines do not provide detailed guidance on technical exposure parameters. The EC guidelines are more complete but are dedicated to screen film systems. Other studies provided reviews on the several exposure parameters that should be included for optimisation, such as tube current, tube voltage and source-to-image distance; however, only explored few of these parameters and not all of them together. One publication explored all parameters together but this was for adults only. Due to lack of literature on exposure parameters for paediatrics, more research is required to guide and harmonise practice.

Optimisation of paediatrics computed radiography for full spine curvature measurements using a phantom: a pilot study

Aim: Optimise a set of exposure factors, with the lowest effective dose, to delineate spinal curvature with the modified Cobb method in a full spine using computed radiography (CR) for a 5-year-old paediatric anthropomorphic phantom. Methods: Images were acquired by varying a set of parameters: positions (antero-posterior (AP), posteroanterior (PA) and lateral), kilo-voltage peak (kVp) (66-90), source-to-image distance (SID) (150 to 200cm), broad focus and the use of a grid (grid in/out) to analyse the impact on E and image quality (IQ). IQ was analysed applying two approaches: objective [contrast-to-noise-ratio/(CNR] and perceptual, using 5 observers. Monte-Carlo modelling was used for dose estimation. Cohen’s Kappa coefficient was used to calculate inter-observer-variability. The angle was measured using Cobb’s method on lateral projections under different imaging conditions. Results: PA promoted the lowest effective dose (0.013 mSv) compared to AP (0.048 mSv) and lateral (0.025 mSv). The exposure parameters that allowed lower dose were 200cm SID, 90 kVp, broad focus and grid out for paediatrics using an Agfa CR system. Thirty-seven images were assessed for IQ and thirty-two were classified adequate. Cobb angle measurements varied between 16°±2.9 and 19.9°±0.9. Conclusion: Cobb angle measurements can be performed using the lowest dose with a low contrast-tonoise ratio. The variation on measurements for this was ±2.9° and this is within the range of acceptable clinical error without impact on clinical diagnosis. Further work is recommended on improvement to the sample size and a more robust perceptual IQ assessment protocol for observers.

Mots(dits) écrits:formes et valeurs de la diffusion des idées au 18ème siècle, au Portugal

Les rapports complexes entre les différentes façons de faire circuler les idées et les informations ne datent pas de nos jours. A toutes les époques, les messages qui circulent emploient toutes sortes de véhicules et de langages, très souvent complémentaires. Ces véhicules et ces langages n'ont peut-être rien d'extraordinaire. Ils appartiennent au monde des gestes de tous les jours, des gestes qui se répètent et dont la répétition est elle-même importante pour la construction du sens de chaque message. Ces gestes qui sont répétés, qui sont attendus et qui sont reconnus incluent des sons, des images, des comportements, des mots, ou des citations. Il y a donc un rapport qui s'y établit entre répétition et nouveauté, rapport dans lequel la répétition fournit chaque fois une nouvelle information, même si elle est déjà attendue, tandis que leur absence peut représenter l'anxiété, ou même le scandale.