The Dunkl-Coulomb problem in the plane

The Dunkl-Coulomb system in the plane is considered. The model is defined in terms of the Dunkl Laplacian, which involves reflection operators, with a $r^{-1}$ potential. The system is shown to be maximally superintegrable and exactly solvable. The spectrum of the Hamiltonian is derived algebraically using a realization of $\mathfrak{so}(2,1)$ in terms of Dunkl operators. The symmetry operators generalizing the Runge-Lenz vector are constructed. On eigenspaces of fixed energy, the invariance algebra they generate is seen to correspond to a deformation of $\mathfrak{su}(2)$ by reflections. The exact solutions are given as products of Laguerre polynomials and Dunkl harmonics on the circle.Comment: Two-columns, 6 p

Tapered, tubular polyester fabric

A tapered tubular polyester sleeve is described to serve as the flexible foundation for a spacesuit limb covering. The tube has a large end and a small end with a length to be determined. The ratio of taper is also determined by scale factors. All the warp yarns extend to the large end. A requisite number of warp yarns extend the full length of the sleeve. Other warp yarns extend from the large end but are terminated along the length of the sleeve. It is then woven with a filling yarn which extends in a full circle along the full length of the sleeve to thereby define the tapered sleeve. The sleeve after fabrication is then placed on a mandrel, heated in an oven, and then attached to the arm or other limb of the spacesuit

Initiation et propagation de la corrosion dans un élément de béton armé

La corrosion des aciers d’armatures résultant de la pénétration des ions chlorure est un problème important qui réduit de manière significative la durée de vie des structures en béton armé exposées à un environnement maritime ou à des sels de déglaçage. Ce mémoire présente une étude de l’initiation de la corrosion sur des éprouvettes de mortier armé ainsi qu’une étude du comportement de barres d’armature corrodées. L’objectif général des travaux de maîtrise était d’étudier l’influence réelle de la minéralogie du ciment sur les mécanismes d’initiation de la corrosion des armatures. En plus de contribuer à l’élaboration d’un outil de prédiction de la durée de vie des ouvrages en béton armé exposés à la pénétration des ions chlorure, ce projet a permis de générer des informations permettant aux ingénieurs de la pratique et aux gestionnaires d’ouvrages d’optimiser la formulation des bétons et d’améliorer la durabilité des structures. Le projet était séparé en deux parties. La première partie portait sur l’identification d’une concentration seuil en ions chlorure requise pour initier la corrosion. Les éprouvettes de mortier ont été soumises à des conditions d’expositions contrôlées (cycles de mouillage-séchage). L’évolution de la corrosion a été suivie par des méthodes électrochimiques non-destructives. Les différents facteurs à l’étude ont été le rapport eau sur ciment (e/c), la minéralogie du ciment et le type de préparation des barres d’armature. Les résultats de l’étude de la pénétration des ions chlorure dans les matériaux cimentaires et de sa conséquence sur l’initiation de la corrosion sont présentés. La deuxième partie du projet était d’étudier l’effet de la corrosion sur les propriétés mécaniques des armatures. Les résultats de la mise en traction de barres ayant des degrés de corrosion spécifiques sont également présentés. Selon les résultats obtenus, une diminution du rapport e/c et une augmentation de la teneur en C3A ont été deux facteurs favorisant un temps d’initiation de la corrosion plus élevé. De plus, les barres préparées au jet de sable ont offert une meilleure résistance à la corrosion que les barres brossées. En outre, le temps de fissuration des éprouvettes semblaient être indépendant du rapport e/c et de la minéralogie (teneur en C3A). La concentration critique en ions chlorure totaux requise pour initier la corrosion, trouvée au cours de l’étude, a été d’environ 0,3 % en masse de mortier sec ou 1,2 % en masse de ciment. Cette concentration seuil a pu être évaluée avec précision à l’aide d’éprouvettes avec et sans barres. De plus, la concentration critique a semblé indépendante de la teneur en C3A, du type de préparation de barres (brossé ou préparé au jet de sable) et du rapport e/c.Chloride-induced corrosion of steel reinforcement is an important issue that greatly decreases the service life of all concrete structures exposed to marine environments or de-icing salts. This study analysed the phenomenon of corrosion initiation on reinforced mortar specimens and the behavior of several corroded reinforcing bars. The main objective of the study was to observe the actual influence of cement mineralogy on the various mechanisms of corrosion initiation on steel reinforcement. Contributing to the elaboration of a tool that will be able to predict the service life of a reinforced concrete structures exposed to chlorides, this research also allowed to put forward new information for the civil engineering community, helping engineers and owners optimizing concrete formulations, and improving the durability of concrete constructions. The project was divided in two parts. The first one is aimed at isolating a threshold concentration of chloride-ions that would initiate corrosion. The mortar specimens were exposed to chloride-ions in a controlled environment, by chloride ponding, and the evolution of corrosion was observed with non-destructive electrochemical measurements. Different factors were taken into consideration during these tests: the water/cement ratio, the cement mineralogy, and the various type of reinforcing bars preparation. Going trough this paper, you will learn about the consequences that come from the variation of these factors on the corrosion initiation. The second part of the project studied the effects of corrosion on the mechanical properties of steel reinforcement. The data that resulted from the traction tests, on the bars, at different corrosion levels, are also presented in this document. According to the results of the study, reducing the water/cement ratio and increasing the C3A content led to a longer corrosion initiation time. As for the cracking time of the different mortar specimens, it appeared to be independent from these two factors. Moreover, sandblasted bars were found to be a lot more resistant to corrosion than the brushed bars. In the end, the critical concentration of chloride-ions was found to be around 0.3% by weight of dry mortar or 1.2% by weight of cement. This threshold value was precisely evaluated studying different specimens with and without bars. Furthermore, this threshold value seems independent of the concentration of C3A, the type of bar preparation or the water/cement ratio

Functionalized polyhydroquinolines from amino acids using a key one-pot cyclization cascade and application to the synthesis of (±)-Δ7-mesembrenone

Substituted polyhydroquinolines are ubiquitous skeletal cores found in drugs and bioactive natural products. As a new route to access this motif, we successfully developed a one-pot cyclization cascade with high chemocontrol and diastereoselectivi-ty. The sequence generates two cycles, three carbon-carbon bonds, and an all-carbon quaternary center in a highly conver-gent process. Functionalized polyhydroquinolines and congeners are accessible from commercially available amino acids. This versatile and robust strategy was applied to the synthesis of (±)-D7-mesembrenon

Direct inscription of on-surface waveguides in polymers using a mid-ir fiber laser

A detailed study of photo-inscribed optical waveguides in PMMA and polycarbonate using a mid-IR laser is presented. The wavelength of the laser is tuned near the absorption peaks of stretching C-H molecular bonds and the focused beam is scanned onto the surface of planar polymer samples. For the first time, we report the formation of optical waveguides in both polymers through resonant absorption of the laser beam. The optical properties of the waveguides were thoroughly assessed. An elliptic Gaussian mode is guided at the surface of both polymers. Insertion losses of 3.1 dB for a 30 mm long on-surface waveguide inscribed in PMMA were recorded. Such waveguides can interact with the external medium through evanescent coupling. As a proof of concept, the surface waveguides are used as highly sensitive refractometric sensors. An attenuation dynamical range of 35 dB was obtained for a liquid that matches the index of the PMMA substrate. Our results pave the way for large scale manufacturing of low cost biocompatible photonic devices

Quelles pratiques différenciées pour l’enseignement de l’orthographe lexicale ? Une recension des écrits

Malgré la quantité d’écrits sur la différenciation pédagogique, peu d’entre eux visent à appliquer son cadre conceptuel à des contenus scolaires. Cet article propose de croiser les pratiques en orthographe lexicale et ce cadre. Une recension des écrits a été effectuée dans différentes bases de données. L’anasynthèse a été employée pour analyser les données recueillies et élaborer une modélisation de la différenciation en orthographe lexicale. De nombreuses pistes de différenciation pédagogique sont proposées à la suite de cette catégorisation dans les quatre axes de la différenciation pédagogique : contenu,processus, structure et production

Graph Positional and Structural Encoder

Positional and structural encodings (PSE) enable better identifiability of nodes within a graph, as in general graphs lack a canonical node ordering. This renders PSEs essential tools for empowering modern GNNs, and in particular graph Transformers. However, designing PSEs that work optimally for a variety of graph prediction tasks is a challenging and unsolved problem. Here, we present the graph positional and structural encoder (GPSE), a first-ever attempt to train a graph encoder that captures rich PSE representations for augmenting any GNN. GPSE can effectively learn a common latent representation for multiple PSEs, and is highly transferable. The encoder trained on a particular graph dataset can be used effectively on datasets drawn from significantly different distributions and even modalities. We show that across a wide range of benchmarks, GPSE-enhanced models can significantly improve the performance in certain tasks, while performing on par with those that employ explicitly computed PSEs in other cases. Our results pave the way for the development of large pre-trained models for extracting graph positional and structural information and highlight their potential as a viable alternative to explicitly computed PSEs as well as to existing self-supervised pre-training approaches

Nonlinear increase, invisibility, and sign inversion of a localized fs-laser-induced refractive index change in crystals and glasses

Multiphoton absorption via ultrafast laser focusing is the only technology that allows a three-dimensional structural modification of transparent materials. However, the magnitude of the refractive index change is rather limited, preventing the technology from being a tool of choice for the manufacture of compact photonic integrated circuits. We propose to address this issue by employing a femtosecond-laser-induced electronic band-gap shift (FLIBGS), which has an exponential impact on the refractive index change for propagating wavelengths approaching the material electronic resonance, as predicted by the Kramers–Kronig relations. Supported by theoretical calculations, based on a modified Sellmeier equation, the Tauc law, and waveguide bend loss calculations, we experimentally show that several applications could take advantage of this phenomenon. First, we demonstrate waveguide bends down to a submillimeter radius, which is of great interest for higher-density integration of fs-laser-written quantum and photonic circuits. We also demonstrate that the refractive index contrast can be switched from negative to positive, allowing direct waveguide inscription in crystals. Finally, the effect of the FLIBGS can compensate for the fs-laser-induced negative refractive index change, resulting in a zero refractive index change at specific wavelengths, paving the way for new invisibility applications