Embeddings of locally finite metric spaces into Banach spaces

We show that if X is a Banach space without cotype, then every locally finite metric space embeds metrically into X.Comment: 6 pages, to appear in Proceedings of the AM

Tight embeddability of proper and stable metric spaces

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for $p\in [1,\infty]$, every proper subset of $L_p$ is almost Lipschitzly embeddable into a Banach space $X$ if and only if $X$ contains uniformly the $\ell_p^n$'s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.Comment: 19 page

Towards an analytical theory of the third-body problem for highly elliptical orbits

When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the altitude of the satellite becomes high, which is the case around the apocentre of this type of orbit. For several reasons, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and therefore limited to quasi-circular orbits [17, 25]. On the other hand, the time-dependency due to the motion of the third-body is often neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the disturbing function into a finite polynomial using Fourier expansions of elliptic motion functions in multiple of the satellite's eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, we show how to perform a normalization of the expanded Hamiltonian by means of a time-dependent Lie transformation which aims to eliminate periodic terms. The difficulty lies in the fact that the generator of the transformation must be computed by solving a partial differential equation involving variables which are linear with time and the eccentric anomaly which is not time linear. We propose to solve this equation by means of an iterative process.Comment: Proceedings of the International Symposium on Orbit Propagation and Determination - Challenges for Orbit Determination and the Dynamics of Artificial Celestial Bodies and Space Debris, Lille, France, 201

Comparison between alpha- and beta-carbonic anhydrases: can Zn(His)3(H2O) and Zn(His)(Cys)2(H2O) sites lead to equivalent enzymes?

International audienceLarge models of alpha- and beta-carbonic anhydrases were compared using DFT calculations. They indicate similar acidity of coordinated water molecule and zinc affinity. This explains their similar mechanism of action, despite the wide difference in their first coordination sphere

Unbalanced Fractional Cointegration and the No-Arbitrage Condition on Commodity Markets

Technical abstract: A necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Nonetheless, in some cases, the apparent unbalance of integration orders of the observables can be misleading and the cointegration theory applies all the same. This situation refers to unbalanced cointegration in the sense that balanced long run relationship can be recovered by an appropriate filtering of one of the time series. In this paper, we suggest a local Whittle estimator of bivariate unbalanced fractional cointegration systems. Focusing on a degenerating band around the origin, it estimates jointly the unbalance parameter, the long run coefficient and the integration orders of the regressor and the cointegrating errors. Its consistency is demonstrated for the stationary regions of the parameter space and a finite sample analysis is conducted by means of Monte Carlo experiments. An application to the no-arbitrage condition between crude oil spot and futures prices is proposed to illustrate the empirical relevance of the developed estimator. Non-technical abstract: The no-arbitrage condition between spot and future prices implies an analogous condition on their underlying volatilities. Interestingly, the long memory behavior of the volatility series also involves a long-run relationship that allows to test for the no-arbitrage condition by means of cointegration techniques. Unfortunately, the persistent nature of the volatility can vary with the future maturity, thereby leading to unbalanced integration orders between spot and future volatility series. Nonetheless, if a balanced long-run relationship can be recovered by an appropriate filtering of one of the time series, the cointegration theory applies all the same and unbalanced cointegration operates between the raw series. In this paper, we introduce a new estimator of unbalanced fractional cointegration systems that allows to test for the no-arbitrage condition between the crude oil spot and futures volatilities

Fantasme(s) d’emprisonnement, persécution et délire d’organisation dans la littérature sadienne

Le nom de Sade s’est imposé comme une évidence dès la lecture du titre « Articuler le fantasme et l’histoire ». Pourquoi Sade apparaît-il d’emblée légitime quand il est question de fantasme et d’histoire ? Ce qui frappe dans un premier temps, dès que l’on prononce le nom de Sade, c’est l’imaginaire qui s’est développé et se développe encore. Il cristallise autour de lui l’attention puis toutes les inventions et rumeurs possibles. Les seuls crimes dont il a été reconnu coupable sont la flagell..

Advanced modelling for design helping of heterogeneous CLT panels in bending

International audienceCross Laminated Timber (CLT) panels are more and more common in timber construction. When submitted to out-of-plane loads, their main structural issue is the low transverse shear strength of cross layers which leads to rolling shear failure [1, 2]. The absence of specific standards yields to CLT panels having lateral boards glued each other or not, depending on the producer. The resulting discontinuities in the non-gluing case influence the global mechanical response [3]. In addition, the timber construction market requires new technical solutions for CLT. Periodic voids within the panel lead to lighter and more thermally efficient floors. However this geometry increases the panel’s heterogeneity and the difficulties in predicting the actual bending behaviour, especially the shear effects.In the first part of this work we focused our attention to a CLT layer having weak heterogeneities, namely the gaps between boards. These heterogeneities are taken into account by means of a (fictitious) equivalent and homogeneous CLT layer which mechanical properties are defined with respect to the board’s reference frame. Such an equivalent layer is combined with the exact 3D solution for laminated plates in bending [4] and a failure criterion for wood [5]. The predicted behaviour is in good agreement with a reference experimental test [6] in terms of global stiffness and variation of failure modes within the apparent elastic regime. The validated model is therefore used to investigate the influence of varying some panel’s properties on the bending response.Innovative CLT panels having periodic voids (filled by an isolating material) are already in production. An experimental campaign proved how this lay-up increases their shear weakness. The ratio wood/void can approximate the reduced elastic properties of these strongly heterogeneous panels. This approach has been already used [2] with design method for CLT in bending [7] and can be simply implemented in the Equivalent – Layer model. As a starting point we aim to compare the experimental behaviour with the predicted one using reduced mechanical properties by the ratio wood/void. These properties are combined with the model developed for weak heterogeneities and design methods for CLT in bending [7, 8].Nevertheless, such a simplified approach can’t reproduce the complexity of stresses’ and strains’ distribution, especially transverse shear ones. Therefore a more accurate model is currently in development. This solution can precisely predict the influence of high heterogeneities by means of a periodic homogenization scheme. Panel’s reduced elastic properties (EI – GA) derived with such an advanced modelling can be finally used for practical design of bending members

Évolution typologique et technique des meules du Néolithique au Moyen Âge

Les deux principaux axes du programme fixé pour cette année 2016 ont été atteints. Il s’agissait dans un premier temps de finaliser le travail en région Centre-Val de Loire et dans un second temps de retravailler et de fusionner les bases de données « rotative » et « va-et-vient » développées par le PCR ces dernières années. L’année 2016 a permis de poursuivre l’inventaire et la contextualisation des outils de mouture (dont l’attribution chronologique est assurée) étudiés dans la région Centr..

Comportement en flexion de panneaux en bois lamellé croisé hétérogènes

National audienceDans le domaine de la construction bois, les panneaux en bois massif lamellés croisés (CLT – Cross Laminated Timber) sont de plus en plus utilisés en tant que plancher ou toiture. Ils sont composés de plusieurs couches en bois empilées et collées de façon croisée, pour obtenir des bonnes propriétés mécaniques et hygrométriques dans les deux directions.Un enjeu technologique en développement est d’enlever du bois des planchers CLT et le remplacer avec du matériau isolant afin de rendre les panneaux plus légers et plus performants acoustiquement et thermiquement. L’utilisation de ces nouveaux planchers est encore limitée, à cause d’une connaissance insuffisante de leur comportement mécanique en flexion.Des essais de flexion 4-points sur des planchers CLT massifs et aérés ont été conduits. Cette campagne essais a montrée l’augmentation des effets de cisaillement quand le pourcentage des vides augmente. En plus, le plancher le plus aéré a montré des modes de ruine complexes liées aux effets de cisaillement roulant (RT) et traction perpendiculaire aux fibres difficiles à prévoir avec les méthodes simplifiées des ingénieurs. Ensuite, les planches en bois des planchers ont été testées pour déterminer les raideurs élastiques et les résistances. Les essais de caractérisation comprennent : traction parallèle aux fibres, compression selon les trois directions et cisaillement roulant.Une première approche pour reproduire le comportement des planchers CLT aérés peut être celui d’utiliser des méthodes pour les CLT massifs et réduire les propriétés mécanique du bois issues des essais de caractérisation par le pourcentage du vide. Les deux méthodes pour le calcul en flexion choisies sont : la méthode d’analogie du cisaillement (Kreuzinger, 1999) adoptée par la norme allemande (DIN, 2004) et un modèle développé récemment qui combine une solution analytique 3D (Pagano, 1970) avec une couche CLT homogène équivalente (Franzoni et al, 2015).Une modélisation plus avancée du comportement en flexion de ces panneaux très hétérogènes en bois est en cours. Le modèle choisi est un schéma d’homogénéisation périodique géré par une théorie de plaque pour les stratifiés (Lebée, 2012). À ce moment, seulement la raideur en flexion a été calculée avec cette méthode. Cette modélisation avancée permettra de déterminer les principaux paramètres pour concevoir ces nouveaux planchers aérés en bois, comme la raideur en flexion, la raideur en cisaillement, le chargement critique et le mode de ruine associé