Codes correcteurs sur des anneaux de Öre multivariés

16 pagesOn étudie dans ce papier certains anneaux de Öre multivariés sur un corps fini. L'adaptation de l'algorithme de Buchberger dans ce cadre non commutatif permet de manipuler les idéaux de ces anneaux, notamment les idéaux bilatères. Ces outils permettent de construire et d'étudier des codes tordus sur ces anneaux de polynômes multivariés et en particulier de fournir la matrice génératrice du code sous forme systématique

Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases

Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{\'e} system) are determined by an asymptotic analysis as the thickness ($2\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\varepsilon$. Optimizing $k$ for each chosen $\varepsilon$, we find power laws for $k$ in function of $\varepsilon$ that provide the smallest eigenvalues of the scalar reductions.Corresponding eigenpairs generate quasimodes for the 3D Lam{\'e} system by means of several reconstruction operators, including boundary layer terms. Numerical experiments demonstrate that in many cases the constructed eigenpair corresponds to the first eigenpair of the Lam{\'e} system.Geometrical conditions are necessary to this approach: The Gaussian curvature has to be nonnegative and the azimuthal curvature has to dominate the meridian curvature in any point of the midsurface. In this case, the first eigenvector admits progressively larger oscillation in the angular variable as $\varepsilon$ tends to $0$. Its angular frequency exhibits a power law relationof the form $k=\gamma \varepsilon^{-\beta}$ with $\beta=\frac14$ in the parabolic case (cylinders and trimmed cones), and the various $\beta$s $\frac25$, $\frac37$, and $\frac13$ in the elliptic case.For these cases where the mathematical analysis is applicable, numerical examples that illustrate the theoretical results are presented

High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2$\epsilon$) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue $\lambda$($\epsilon$) and the eigenvector angular frequency k($\epsilon$) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on the other parts. First, the scalar Laplace operator for acoustics is addressed, for which k($\epsilon$) is always zero. In contrast to it, for the Lam{\'e} system of linear elasticity several different types of shells are defined, characterized by their geometry, for which k($\epsilon$) tends to infinity as $\epsilon$ tends to zero. For two families of shells: cylinders and elliptical barrels we explicitly provide $\lambda$($\epsilon$) and k($\epsilon$) and demonstrate by numerical examples the different behavior as $\epsilon$ tends to zero

Skew codes of prescribed distance or rank

International audienceIn this paper we propose two methods to produce block codes of prescribed rank or distance. Following [4, 5] we work with skew polynomial rings of automorphism type and the codes we investigate are ideals in quotients of this ring. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) which is reviewed in the first section

Emmanuel Grison. Notre père

Papa aimait travailler. Il ne nous parlait pas beaucoup de ce qu’il faisait, ni des personnes qu’il était amené à rencontrer, mais j’ai toujours senti combien il était passionné par son activité professionnelle. J’ai souvenir, par exemple, des longues heures passées, même le dimanche, pour préparer son cours de Chimie à l’X. Lorsqu’après avoir pris sa retraite il s’est intéressé à l’histoire de l’École polytechnique, puis à la correspondance des chimistes Guyton de Morvau et Kirwan, et enfin ..

Superficial cancer of the stomach

Le cancer superficiel de l’estomac est un cancer limité à la muqueuse ou à la sous-muqueuse (T1). L’absence d’invasion de la musculaire muqueuse diminue le risque d’envahissement ganglionnaire et permet d’envisager un traitement endoscopique. Le risque de métastases ganglionnaires est corrélé à la taille de la tumeur, à l’envahissement en profondeur de la lésion et à l’aspect endoscopique de la lésion. Le traitement endoscopique consiste à réaliser, après repérage de la lésion, une dissection sous-muqueuse de celle-ci, et cela afin de permettre une résection en monobloc. Cette technique, limitée à certains centres, permet d’envisager un traitement curatif endoscopique de ces tumeurs et doit être suivie d’une surveillance rapprochée endoscopique

Imaging in pulmonary hypertension: Focus on the role of echocardiography

SummaryPatients with pulmonary hypertension must be evaluated using a multimodality approach to ensure a correct diagnosis and basal evaluation as well as a prognostic assessment. Beyond the assessment of pulmonary pressures, the echocardiographical examination allows the evaluation of right ventricular adaptation to elevated afterload. Numbers of variables are commonly used in the assessment of the pulmonary hypertension patient in order to detect changes in right heart geometry, right-to-left interaction and right ventricular dysfunction. Whereas an isolated change in one echocardiographical variable is not meaningful, multiple echocardiographical variable modifications together provide accurate information. In this review, we will link pulmonary hypertension pathophysiological changes with echocardiographical indices and describe the clinical implications of echocardiographical findings

Services climatiques pour l'adaptation au changement climatique

National audienceLe changement climatique constitue une problématique majeure perceptible dès aujourd'hui ; la société et l'ensemble de ses acteurs peuvent percevoir la nécessité de l'adaptation à cette nouvelle situation