Séries universelles dans CN et sur les surfaces de Riemann non compactes

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Surfaces de Riemann compactes et formule de trace d'Eichler

Dans ce mémoire, nous étudierons quelques propriétés algébriques, géométriques et topologiques des surfaces de Riemann compactes. Deux grand sujets seront traités. Tout d'abord, en utilisant le fait que toute surface de Riemann compacte de genre g plus grand ou égal à 2 possède un nombre fini de points de Weierstrass, nous allons pouvoir conclure que ces surfaces possèdent un nombre fini d'automorphismes. Ensuite, nous allons étudier de plus près la formule de trace d'Eichler. Ce théorème nous permet de trouver le caractère d'un automorphisme agissant sur l'espace des q-différentielles holomorphes. Nous commencerons notre étude en utilisant la quartique de Klein. Nous effectuerons un exemple de calcul utilisant le théorème d'Eichler, ce qui nous permettra de nous familiariser avec l'énoncé du théorème. Finalement, nous allons démontrer la formule de trace d'Eichler, en prenant soin de traiter le cas où l'automorphisme agit sans point fixe séparément du cas où l'automorphisme possède des points fixes.

Tailoring molecule nanostructures on insulating surfaces investigated by non-contact atomic force microscopy

Self-assembled molecular structures were investigated on insulating substrate surfaces using non-contact atomic force microscopy. Both, substrate preparation and molecule deposition, took place under ultra-high vacuum conditions. First, C60 molecules were investigated on the TiO2 (110) surface. This surface exhibits parallel running troughs at the nanometer scale, which strongly steer the assembly of the molecules. This is in contrast to the second investigated surface. The CaF2 (111) surface is atomically flat and the molecular assemblyrnwas observed to be far less affected by the surface. Basically different island structures were observed to what is typically know. Based on extensive experimental studies and theoretical considerations, a comprehensive picture of the processes responsible for the island formation of C60 molecules on this insulating surfaces was developed. The key process for the emergence of the observed novel island structures was made out to be the dewetting of molecules from the substrate. This new knowledge allows to further understand andrnexploit self-assembly techniques in structure fabrication on insulating substrate surfaces. To alter island formation and island structure, C60 molecules were codeposited with second molecule species (PTCDI and SubPc) on the CaF2 (111) surface. Depending on the order of deposition, quiet different structures were observed to arise. Thus, these are the first steps towards more complex functional arrangements consisting of two molecule species on insulating surfaces.

Detection of cavitated approximal surfaces using cone beam CT and intraoral receptors

Objectives: The aim of this study was to compare cone beam CT (CBCT) in a small field of view (FOV) with a solid-state sensor and a photostimulable phosphor plate system for detection of cavitated approximal surfaces. Methods: 257 non-filled approximal surfaces from human permanent premolars and molars were recorded by two intraoral digital receptors, a storage phosphor plate (Digora Optime, Soredex) and a solid-state CMOS sensor (Digora Toto, Soredex), and scanned in a cone beam CT unit (3D Accuitomo FPD80, Morita) with a FOV of 4 cm and a voxel size of 0.08 mm. Image sections were carried out in the axial and mesiodistal tooth planes. Six observers recorded surface cavitation in all images. Validation of the true absence or presence of surface cavitation was performed by inspecting the surfaces under strong light with the naked eye. Differences in sensitivity, specificity and agreement were estimated by analysing the binary data in a generalized linear model using an identity link function. Results: A significantly higher sensitivity was obtained by all observers with CBCT (p,0.001), which was not compromised by a lower specificity. Therefore, a significantly higher overall agreement was obtained with CBCT (p,0.001). There were no significant differences between the Digora Optime phosphor plate system and the Digora Toto CMOS sensor for any parameter. Conclusions: CBCT was much more accurate in the detection of surface cavitation in approximal surfaces than intraoral receptors. The differences are interpreted as clinically significant. A CBCT examination performed for other reasons should also be assessed for approximal surface cavities in teeth without restorations. © 2013 The British Institute of Radiology.

Nanostructured metal oxides as adsorbents and photocatalysts

This research underlines the extensive application of nanostructured metal oxides in environmental systems such as hazardous waste remediation and water purification. This study tries to forge a new understanding of the complexity of adsorption and photocatalysis in the process of water treatment. Sodium niobate doped with a different amount of tantalum, was prepared via a hydrothermal reaction and was observed to be able to adsorb highly hazardous bivalent radioactive isotopes such as Sr2+ and Ra2+ions. This study facilitates the preparation of Nb-based adsorbents for efficiently removing toxic radioactive ions from contaminated water and also identifies the importance of understanding the influence of heterovalent substitution in microporous frameworks. Clay adsorbents were prepared via a two-step method to remove anionic and non-ionic herbicides from water. Firstly, layered beidellite clay was treated with acid in a hydrothermal process; secondly, common silane coupling agents, 3-chloro-propyl trimethoxysilane or triethoxy silane, were grafted onto the acid treated samples to prepare the adsorption materials. In order to isolate the effect of the clay surface, we compared the adsorption property of clay adsorbents with ƒ×-Al2O3 nanofibres grafted with the same functional groups. Thin alumina (£^-Al2O3) nanofibres were modified by the grafting of two organosilane agents 3-chloropropyltriethoxysilane and octyl triethoxysilane onto the surface, for the adsorptive removal of alachlor and imazaquin herbicides from water. The formation of organic groups during the functionalisation process established super hydrophobic sites along the surfaces and those non-polar regions of the surfaces were able to make close contact with the organic pollutants. A new structure of anatase crystals linked to clay fragments was synthesised by the reaction of TiOSO4 with laponite clay for the degradation of pesticides. Based on the Ti/clay ratio, these new catalysts showed a high degradation rate when compared with P25. Moreover, immobilized TiO2 on laponite clay fragments could be readily separated out from a slurry system after the photocatalytic reaction. Using a series of partial phase transition methods, an effective catalyst with fibril morphology was prepared for the degradation of different types of phenols and trace amount of herbicides from water. Both H-titanate and TiO2-(B) fibres coated with anatase nanocrystal were studied. When compared with a laponite clay photocatalyst, it was found that anatase dotted TiO2-(B) fibres prepared by a 45 h hydrothermal treatment followed by calcination were not only superior in performance in photocatalysis but could also be readily separated from a slurry system after photocatalytic reactions. This study has laid the foundation for the development of the ability to fabricate highly efficient nanostructured solids for the removal of radioactive ions and organic pollutants from contaminated water. These results now seem set to contribute to the development of advanced water purification devices in the future. These modified nanostructured materials with unusual properties have broadened their application range beyond their traditional use as adsorbents, to also encompass the storage of nuclear waste after concentrating from contaminated water.

Application of high voltage, high frequency pulsed electromagnetic field on cortical bone tissue

Over the last few decades, electric and electromagnetic fields have achieved important role as stimulator and therapeutic facility in biology and medicine. In particular, low magnitude, low frequency, pulsed electromagnetic field has shown significant positive effect on bone fracture healing and some bone diseases treatment. Nevertheless, to date, little attention has been paid to investigate the possible effect of high frequency, high magnitude pulsed electromagnetic field (pulse power) on functional behaviour and biomechanical properties of bone tissue. Bone is a dynamic, complex organ, which is made of bone materials (consisting of organic components, inorganic mineral and water) known as extracellular matrix, and bone cells (live part). The cells give the bone the capability of self-repairing by adapting itself to its mechanical environment. The specific bone material composite comprising of collagen matrix reinforced with mineral apatite provides the bone with particular biomechanical properties in an anisotropic, inhomogeneous structure. This project hypothesized to investigate the possible effect of pulse power signals on cortical bone characteristics through evaluating the fundamental mechanical properties of bone material. A positive buck-boost converter was applied to generate adjustable high voltage, high frequency pulses up to 500 V and 10 kHz. Bone shows distinctive characteristics in different loading mode. Thus, functional behaviour of bone in response to pulse power excitation were elucidated by using three different conventional mechanical tests applying three-point bending load in elastic region, tensile and compressive loading until failure. Flexural stiffness, tensile and compressive strength, hysteresis and total fracture energy were determined as measure of main bone characteristics. To assess bone structure variation due to pulse power excitation in deeper aspect, a supplementary fractographic study was also conducted using scanning electron micrograph from tensile fracture surfaces. Furthermore, a non-destructive ultrasonic technique was applied for determination and comparison of bone elasticity before and after pulse power stimulation. This method provided the ability to evaluate the stiffness of millimetre-sized bone samples in three orthogonal directions. According to the results of non-destructive bending test, the flexural elasticity of cortical bone samples appeared to remain unchanged due to pulse power excitation. Similar results were observed in the bone stiffness for all three orthogonal directions obtained from ultrasonic technique and in the bone stiffness from the compression test. From tensile tests, no significant changes were found in tensile strength and total strain energy absorption of the bone samples exposed to pulse power compared with those of the control samples. Also, the apparent microstructure of the fracture surfaces of PP-exposed samples (including porosity and microcracks diffusion) showed no significant variation due to pulse power stimulation. Nevertheless, the compressive strength and toughness of millimetre-sized samples appeared to increase when the samples were exposed to 66 hours high power pulsed electromagnetic field through screws with small contact cross-section (increasing the pulsed electric field intensity) compare to the control samples. This can show the different load-bearing characteristics of cortical bone tissue in response to pulse power excitation and effectiveness of this type of stimulation on smaller-sized samples. These overall results may address that although, the pulse power stimulation can influence the arrangement or the quality of the collagen network causing the bone strength and toughness augmentation, it apparently did not affect the mineral phase of the cortical bone material. The results also confirmed that the indirect application of high power pulsed electromagnetic field at 500 V and 10 kHz through capacitive coupling method, was athermal and did not damage the bone tissue construction.

Assessment of permeable covers for odour reduction in piggery effluent ponds. 2. Field-scale trials

The efficacy of supported covers was investigated under field conditions using a series of prototypes deployed on an anaerobic pond treating typical piggery waste. Research focused on identifying effective cover support materials and deployment methods, quantifying odour reduction, and estimating the life expectancy of various permeable cover materials. Over a 10-month period, median odour emission rates were five to eight times lower from supported straw cover surfaces and a non-woven, spun fibre polypropylene weed control material than from the adjacent uncovered pond surface. While the straw covers visually appeared to degrade very rapidly, they continued to reduce odour emissions effectively. The polypropylene cover appeared to offer advantages from the perspectives of cost, reduced maintenance and ease of manufacture.

Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.

Seeing 'Ghost' Solutions in Stereo Vision

A unique matching is a stated objective of most computational theories of stereo vision. This report describes situations where humans perceive a small number of surfaces carried by non-unique matching of random dot patterns, although a unique solution exists and is observed unambiguously in the perception of isolated features. We find both cases where non-unique matchings compete and suppress each other and cases where they are all perceived as transparent surfaces. The circumstances under which each behavior occurs are discussed and a possible explanation is sketched. It appears that matching reduces many false targets to a few, but may still yield multiple solutions in some cases through a (possibly different) process of surface interpolation.

Analyse de maillages surfaciques par construction et comparaison de modèles moyens et par décomposition par graphes s’appuyant sur les courbures discrètes : application à l’étude de la cornée humaine

Réalisé en cotutelle avec Aix Marseille Université.

The assessment of тт-тт selective stationary phases for two-dimensional HPLC analysis of foods : application to the analysis of coffee

Differences between alkyl, dipole–dipole, hydrogen bonding, and π-π selective surfaces represented by non-resonance and resonance π-stationary phases have been assessed for the separation of ‘Ristretto’ café espresso by employing 2DHPLC techniques with C18 phase selectivity detection. Geometric approach to factor analysis (GAFA) was used to measure the detected peaks (N), spreading angle (β), correlation, practical peak capacity (n_p) and percentage usage of the separations space, as an assessment of selectivity differences between regional quadrants of the two-dimensional separation plane. Although all tested systems were correlated to some degree to the C18 dimension, regional measurement of separation divergence revealed that performance of specific systems was better for certain sample components. The results illustrate that because of the complexity of the ‘real’ sample obtaining a truly orthogonal two-dimensional system for complex samples of natural origin may be practically impossible.

Synthesis and growth of hematite nanodiscs through a facile hydrothermal approach

This study reports a facile hydrothermal method for the synthesis of monodispersed hematite (α-Fe2O3) nanodiscs under mild conditions. The method has features such as no use of surfactants, no toxic precursors, and no requirements of high-temperature decomposition of iron precursors in non-polar solvents. By this method, α-Fe2O3 nanodiscs were achieved with diameter of 50 ± 10 nm and thickness of ~6.5 nm by the hydrolysis of ferric chloride. The particle characteristics (e.g., shape, size, and distribution) and functional properties (e.g., magnetic and catalytic properties) were investigated by various advanced techniques, including TEM, AFM, XRD, BET, and SQUID. Such nanodiscs were proved to show unique magnetic properties, i.e., superparamagnetic property at a low temperature (e.g., 20 K) but ferromagnetic property at a room temperature (~300 K). They also exhibit low-temperature (<623 K) catalytic activity in CO oxidation because of extremely clean surfaces due to non-involvement of surfactants, compared with those spheres and ellipsoids capped by PVP molecules.

Two novel reports of semidry stigmatic surface in Asteraceae

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Geometria e topologia das superfícies através de recorte e colagem

Pós-graduação em Matemática Universitária - IGCE

Comparative stability studies of poly(2-methyl-2-oxazoline) and poly(ethylene glycol) brush coatings

Non-fouling surfaces that resist non-specific adsorption of proteins, bacteria, and higher organisms are of particular interest in diverse applications ranging from marine coatings to diagnostic devices and biomedical implants. Poly(ethylene glycol) (PEG) is the most frequently used polymer to impart surfaces with such non-fouling properties. Nevertheless, limitations in PEG stability have stimulated research on alternative polymers that are potentially more stable than PEG. Among them, we previously investigated poly(2-methyl-2-oxazoline) (PMOXA), a peptidomimetic polymer, and found that PMOXA shows excellent anti-fouling properties. Here, we compare the stability of films self-assembled from graft copolymers exposing a dense brush layer of PEG and PMOXA side chains, respectively, in physiological and oxidative media. Before media exposure both film types prevented the adsorption of full serum proteins to below the detection limit of optical waveguide in situ measurements. Before and after media exposure for up to 2 weeks, the total film thickness, chemical composition, and total adsorbed mass of the films were quantified using variable angle spectroscopic ellipsometry (VASE), X-ray photoelectron spectroscopy (XPS), and optical waveguide lightmode spectroscopy (OWLS), respectively. We found (i) that PMOXA graft copolymer films were significantly more stable than PEG graft copolymer films and kept their protein-repellent properties under all investigated conditions and (ii) that film degradation was due to side chain degradation rather than due to copolymer desorption.