Some isomorphisms for the Brauer groups of a Hopf algebra

Using equivalences of categories we provide isomorphisms between the Brauer groups of different Hopf algebras. As an example, we show that when k is a field of characteristic different from 2 the Brauer groups BC(k,H_4,r_t) for every dual quasitriangular structure r_t on Sweedler's Hopf algebra H_4 are all isomorphic to the direct sum of (k,+) and the Brauer-Wall group of k. We provide an isomorphism between the Brauer group of a Hopf algebra H and the Brauer group of the dual Hopf algebra H^* generalizing a result of Tilborghs. Finally we relate the Brauer groups of H and of its opposite and co-opposite Hopf algebras.Comment: 23 pages, minor changes, one reference adde

Factorizations of skew braces

We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang-Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of It\^{o}'s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang-Baxter equation. Finally, we classify skew braces that contain no non-trivial proper ideals.Comment: 12 page

The Iray Light Transport Simulation and Rendering System

While ray tracing has become increasingly common and path tracing is well understood by now, a major challenge lies in crafting an easy-to-use and efficient system implementing these technologies. Following a purely physically-based paradigm while still allowing for artistic workflows, the Iray light transport simulation and rendering system allows for rendering complex scenes by the push of a button and thus makes accurate light transport simulation widely available. In this document we discuss the challenges and implementation choices that follow from our primary design decisions, demonstrating that such a rendering system can be made a practical, scalable, and efficient real-world application that has been adopted by various companies across many fields and is in use by many industry professionals today

La classe inversée et des podcasts pour favoriser un apprentissage individualisé dans le cadre d’un cours scientifique à population hétéroclite

Comprend des références bibliographiquesCet article traite de la mise en place du dispositif des classes inversées et de la création d’outils pédagogiques (podcasts, plateforme virtuelle, questionnaires) dans le cadre d’un module s’inscrivant dans un cours scientifique, délivré à l’Université libre de Bruxelles, suivi par des étudiants de facultés différentes et d’années différentes. Ce système de la classe inversée fut innovant tant pour les étudiants que pour les enseignants, qui découvraient cette approche pédagogique. Cette expérience fut enrichissante. Elle a permis de solutionner des problèmes rencontrés par les enseignants lors d’un enseignement traditionnel. D’autre part, elle illustre l’intérêt des étudiants à suivre d’autres cours organisés selon ce modèle. En effet, l’évaluation du dispositif a mis en avant des résultats encourageants et prometteurs

Higgs boson as a gluon trigger: the study of QCD in high pile-up environments

In the forthcoming high-luminosity phase of the LHC many of the most interesting measurements for precision QCD studies are hampered by large pile-up conditions, especially at not very high transverse momenta. However, with the recently discovered Higgs boson, which couples in the heavy top limit directly to gluons, we have access to a novel production process to probe QCD by a colour-singlet current. In this study we compare observables in Higgs boson and Drell-Yan production and investigate whether measuring ratios or subtractions can yield results that are stable in high pile-up environments, and yet sensitive to (small-$p_{\text{T}}$) QCD physics in gluon fusion processes. We present results of Monte Carlo event generator calculations for a few specific examples.Comment: 7 pages, 10 figures, DIS2014 conference proceeding