On Z/2Z-extensions of pointed fusion categories

We give a classification of Z/2Z-graded fusion categories whose 0-component is a pointed fusion category. A number of concrete examples is considered.Comment: This article will be published by the Banach Center Publication

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The aim of this study was to map and date glacial flutings with ice flows deviating from the predominating northwesterly ice flow direction in the southern part of Norrbotten County in northern Sweden, and also to investigate if parts of the glacial landscape are older than previously thought. The traditional view is that most landforms in the area were formed during the late Weichselian (W3). Analysis of the new high resolution elevation model (2 m grid) derived from laser scanning was performed after treating the data with a hillshade tool in ArcMap to reveal terrain features such as flutings. The analysis resulted in a map showing four main groups of deviating ice flows (N-S, NO-SV, SO-NV and S-N) and several westerly ice flows. The majority of flutings with deviating ice flows were found in low terrain. This, together with studies suggesting a cold based late Weichselian ice sheet in Norrbotten, implies an old age of the deviating ice flows. The deviating ice flows are interpreted to originate from the first early Weichselian (W1), or predate the onset of the Weichselian glaciation. Some NV-SO flutings were located in high terrain, which implies a younger age relative to the low terrain flutings. They represent the youngest ice flow found in the area, possibly from the second early Weichselian (W2). The new elevation model clearly offers new possibilities for studying small scale landforms and shows that the traditional view of the Weichselian glaciation in northern Swedish needs to be reconsidered

The Correction of Chronologic Series’ Seasonal Fluctuations according to Seasonal Simultaneous Additive and Multiplicative Effects.

Dans cette étude, portant sur l’analyse chronologique des ventes, nous posons le problème de l’existence probable d’une saisonnalité mixte additive et multiplicative. Dans ce contexte, nous montrons par des simulations que la désaisonnalisation selon un schéma additif pur ou un schéma multiplicatif pur introduit un biais dans l’estimation des coefficients et en conséquence dans le calcul de la série Corrigée des Variations Saisonnières (CVS) nécessaire à toute analyse quantitative de la demande. L’utilisation d’une technique de résolution analytique permettant d’estimer simultanément les coefficients de la tendance et les coefficients saisonniers additifs et multiplicatifs fonctionne parfaitement si la chronique est affectée d’une simple tendance linéaire : nous retrouvons bien les coefficients saisonniers théoriques. Enfin, une application au marché de la téléphonie mobile, produit innovant segmenté en deux marchés : professionnel et particulier, permet d’évaluer l’intérêt de cette méthodologie.In this study we set the problem of the probable existence of an additive and multiplicative mixed seasonality. In this context, we show by some simulation that the seasonality correction according to a pure additive or a pure multiplicative scheme leads to biased estimators of the coefficients and, consequently, in the calculation of seasonally adjusted series which is necessary for quantitative demand analysis. The use of an analytical resolution technique allowing to estimate simultaneously the trend coefficients and the additive and multiplicative seasonal coefficients. perfectly works if the series is affected by a simple linear trend .In this case, the estimation gives the theoretical seasonal coefficients. An application study to the mobile phone market, new product split in two markets : professional and individuals allows to evaluate the contribution of the methodology.Seasonality; time series; demand analysis;

Deformation of finite dimensional C*-quantum groupoids

In this work we prove, in full details, that any finite dimensional $C^*$-quantum groupoid can be deformed in order that the square of the antipode is the identity on the base. We also prove that for any $C^*$-quantum groupoid with non abelian base, there is uncountably many $C^*$-quantum groupoids with the same underlying algebra structure but which are not isomorphic to it. In fact, the $C^*$-quantum groupoids are closed in an analog of the procedure presented by D.Nikshych ([N] 3.7) in a more general situation

C*-pseudo-multiplicative unitaries and Hopf C*-bimodules

We introduce C*-pseudo-multiplicative unitaries and concrete Hopf C*-bimodules for the study of quantum groupoids in the setting of C*-algebras. These unitaries and Hopf C*-bimodules generalize multiplicative unitaries and Hopf C*-algebras and are analogues of the pseudo-multiplicative unitaries and Hopf--von Neumann-bimod-ules studied by Enock, Lesieur and Vallin. To each C*-pseudo-multiplicative unitary, we associate two Fourier algebras with a duality pairing, a C*-tensor category of representations, and in the regular case two reduced and two universal Hopf C*-bimodules. The theory is illustrated by examples related to locally compact Hausdorff groupoids. In particular, we obtain a continuous Fourier algebra for a locally compact Hausdorff groupoid.Comment: 50 pages; this is a substantial revision and expansion of the preprint "C*-pseudo-multiplicative unitaries" (arXiv:0709.2995) with many new result

Carta de un oficial en defensa de los militares que dexaron sus cuerpos por agregarse á los Patriotas de las provincias : Y obligaciones de todo español en las actuales circunstancias

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