Sur les prolongements de sous-copules

L’objet du travail est d’étudier les prolongements de sous-copules. Un cas important de l’utilisation de tels prolongements est l’estimation non paramétrique d’une copule par le lissage d’une sous-copule (la copule empirique). Lorsque l’estimateur obtenu est une copule, cet estimateur est un prolongement de la souscopule. La thèse présente au chapitre 2 la construction et la convergence uniforme d’un estimateur bona fide d’une copule ou d’une densité de copule. Cet estimateur est un prolongement de type copule empirique basé sur le lissage par le produit tensoriel de fonctions de répartition splines. Le chapitre 3 donne la caractérisation de l’ensemble des prolongements possibles d’une sous-copule. Ce sujet a été traité par le passé; mais les constructions proposées ne s’appliquent pas à la dépendance dans des espaces très généraux. Le chapitre 4 s’attèle à résoudre le problème suivant posé par [Carley, 2002]. Il s’agit de trouver la borne supérieure des prolongements en dimension 3 d’une sous-copule de domaine fini.

Une évaluation de la dimension de la lumière de boîtiers 0,018" provenant de quatre différents manufacturiers. Existe-t-il un standard dans l’industrie?

Introduction: The objective of this experimental research was to evaluate the slot’s vertical dimension and profile of four different 0.018″ self-ligating brackets and to identify the level of tolerance accepted by manufacturers during the fabrication process. It was then possible to calculate and compare the torque play of those brackets using the measured values and the nominal values. Material and Methods: Twenty-five 0.018″ self-ligating brackets of upper left central incisors from the following manufacturers, Speed® (Strite Industries, Cambridge, Ontario, Canada), InOvationR® (GAC, Bohemia, NY, USA), CarriereLX® (Ortho Organizers, Carlsbad, CA, USA) and SmartClip® (3M Unitek, Monrovia, CA, USA), were evaluated using electron microscopy with 150X images. The height of each bracket was measured at every 100 microns of depth from the lingual wall at five different levels. A Student T test was then used to compare our results with the manufacturer’s stated value of 0.018″. To determine if there was a significant difference between the four manufacturers, analysis of variance (ANOVA) was performed at the significance level of p<0.05. The torque play was then calculated using geometrical formulas. Results: On average, Speed brackets were oversized by 2.7%[MV 0.0185″ (SD:0.002)], InOvationR by 3.7% [MV 0.0187″ (SD:0.002)], CarriereLX by 3.2% [MV 0.0186″ (SD:0.002)] and SmartClipSL by 5.0% [MV 0.0189″ (SD:0.002)]. The height of all brackets was significantly higher than the nominal value of 0.018″ (p<0.001). The slot of SmartClip brackets was significantly larger than those of the other three manufacturers (p<0.001). None of the brackets studied had parallel gingival and occlusal walls; some were convergent and others divergent. These variations can induce a torque play up to 4.5 degrees with a 0.017″x0.025″ wire and 8.0 degrees with a 0.016″x0.022″ wire. Conclusion: All studied brackets were oversized. None of the brackets studied had parallel gingival and occlusal walls and there was no standard between manufacturers for the geometry of their slots. These variations can cause a slight increase of the torque play between the wire and the bracket compared with the nominal value.