Syzygies of differentials of forms

Given a standard graded polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic zero and a graded $k$-subalgebra $A=k[f_1,...,f_m]\subset R$, one relates the module $\Omega_{A/k}$ of K\"ahler $k$-differentials of $A$ to the transposed Jacobian module $\mathcal{D}\subset \sum_{i=1}^n R dx_i$ of the forms $f_1,...,f_m$ by means of a {\em Leibniz map} \Omega_{A/k}\rar \mathcal{D} whose kernel is the torsion of $\Omega_{A/k}$. Letting \fp denote the $R$-submodule generated by the (image of the) syzygy module of $\Omega_{A/k}$ and \fz the syzygy module of $\mathcal{D}$, there is a natural inclusion \fp\subset \fz coming from the chain rule for composite derivatives. The main goal is to give means to test when this inclusion is an equality -- in which case one says that the forms $f_1,...,f_m$ are {\em polarizable}. One surveys some classes of subalgebras that are generated by polarizable forms. The problem has some curious connections with constructs of commutative algebra, such as the Jacobian ideal, the conormal module and its torsion, homological dimension in $R$ and syzygies, complete intersections and Koszul algebras. Some of these connections trigger questions which have interest in their own.Comment: 20 pages. Minor changes after referee's report and updated bibliograph

Active control in an anechoic room : Theory and first simulations

International audienceNoise control and source design require the measurement of sound radiation at low frequencies. Anechoic rooms, which are designed for this purpose, allow echo-free measurements at medium or high frequency but passive wall treatment is less effective at low frequency and in practice no facility provides anechoicity below 50Hz. This paper discusses the applicability of an active control algorithm which has been previously introduced to minimize the echoes from a scattering object to the cancellation of the low frequency wall echoes in an anechoic room including wall-embedded secondary sources. At first the paper discusses, in the general case then for a free half-space as a model case, the algorithm key which consists in estimating the scattered acoustic pressure from total pressure measurements. Boundary Element Method computations are secondly used to simulate estimation and active control of error signals accounting for the low-frequency scattered pressure in an anechoic room. The simulations show that control with a few dozen microphones and noise sources allows a large reduction of the noise scattered from the walls at low-frequency

Towards an active anechoic room

International audienceThis is a presentation of some works in active control. Most of them were conducted by members of the LMA. We will show how these previous works have led to the project which is called ''Active anechoic room'' and is now carried out in the laboratory. The final aim of this project is to develop an active control system in order to increase sound absorption in the LMA anechoic room at low frequencies. Indeed, the characteristics of an anechoic room is to reduce the echoes coming from the walls in a very large frequency range. In the middle and high frequency range, this is very well achieved by covering the walls with absorbing materials. At very low frequencies (below 100Hz for example), this is more difficult but the active control systems are quite efficient at these frequencies and can be used as an additional tool to improve the acoustic performances of the passive system that is the coating on the walls. Apart from its practical applications, the study addresses more general questions related to sound synthesis and representations of sound fields and sources

Polar syzygies in characteristic zero: the monomial case

Given a set of forms f={f_1,...,f_m} in R=k[x_1,...,x_n], where k is a field of characteristic zero, we focus on the first syzygy module Z of the transposed Jacobian module D(f), whose elements are called differential syzygies of f. There is a distinct submodule P of Z coming from the polynomial relations of f through its transposed Jacobian matrix, the elements of which are called polar syzygies of f. We say that f is polarizable if equality P=Z holds. This paper is concerned with the situation where f are monomials of degree 2, in which case one can naturally associate to them a graph G(f) with loops and translate the problem into a combinatorial one. A main result is a complete combinatorial characterization of polarizability in terms of special configurations in this graph. As a consequence, we show that polarizability implies normality of the subalgebra k[f] of R and that the converse holds provided the graph G(f) is free of certain degenerate configurations. One main combinatorial class of polarizability is the class of polymatroidal sets. We also prove that if the edge graph of G(f) has diameter at most 2 then f is polarizable. We establish a curious connection with birationality of rational maps defined by monomial quadrics.Comment: 33 pages, 15 figure

Toward an adjustable nonlinear low frequency acoustic absorber

International audienceThis paper presents experimental results showing that a loudspeaker used as a suspended piston working outside its range of linearity can also be used as a nonlinear acoustic absorber. The main advantage of this technology of absorber is the perspective to adjust independently the device parameters (mass, nonlinear stiffness and damping) according to the operational conditions. To achieve this purpose, quasi-static and dynamic tests have been performed on three types of commercial devices (one with structural modifications), in order to define the constructive characteristics that it should present. An experimental setup has been developed using a one-dimensional acoustic linear system coupled through a box (acting as a weak spring) to a loudspeaker used as a suspended piston acting as an essentially nonlinear oscillator. The tests carried out on the whole vibro-acoustic system have showed the occurrence of the acoustic TET from the acoustic media to the suspended piston and demonstrated the efficiency of this new kind of absorber at low frequencies over a wide frequency range. Moreover, the experimental analyses conducted with different NES masses have confirmed that it is possible to optimize the noise absorption with respect to the excitation level of the acoustic resonator

Le processus de Lisbonne revisité : stratégie Europe 2020 et politiques d'ègalite

El capítulo 5 (páginas 147-174) no es accesible por derechos de autor.Esta monografia recoge las contribuciones, debates y conclusiones del Seminario Internacional sobre las politicas de igualdad y el Proceso de Lisboa que se celebró en Madrid el 23 de junio de 2010, dentro del Proyecto de Investigación nº 151160-LLP-1-2009-1-ES-AJM-CL, financiado por la Comisión Europea. Dicho seminario contó igualmente con el apoyo financiero del Vicerrectorado de lnvestigación (Proyectos nº 2010/00235/001 y n º 2010/00235/002), y del Vicerrectorado de Igualdad y Cooperación de la UCIIIM, así como con el auspicio de la Embajada de la República de Francia en España

Contrôle passif du bruit par pompage énergétique

L'association d'un absorbeur nonlinéaire à un système primaire linéaire permet d'observer le phénomène de transfert énergétique ciblé (également appelé pompage énergétique) et l'application de ce concept à l'acoustique correspond à une nouvelle technique passive de réduction du bruit. Un montage expérimental académique a été développé en utilisant l'air à l'intérieur d'un tube en tant que milieu acoustique primaire, une fine membrane circulaire visco-élastique en tant qu'oscillateur à raideur essentiellement cubique et l'air contenu dans une boîte de grande taille pour assurer un couplage faible entre ces deux éléments. Ce papier s'appuie principalement sur des résultats expérimentaux. Le pompage énergétique est visible sur un des régimes observés sous excitation harmonique, mais également lors des oscillations libres du système. En effet, à partir d'un certain seuil d'énergie initiale, l'extinction sonore dans le tube suit une décroissance quasi-linéaire beaucoup plus rapide que la décroissance classique exponentielle et pendant laquelle l'énergie acoustique du milieu primaire est irréversiblement transférée et dissipée dans la membrane

Measuring farmland biodiversity

About one-third of the world’s land surface is used for farming, a fact that bears important implications for biodiversity. In Europe, for instance, an estimated 50 percent of all wild species are reliant on agricultural habitats, while agricultural productivity often depends on the presence or absence of particular species. Despite this close coupling, surprisingly little is known about the status and evolution of farmland biodiversity. A team of European and African researchers, hoping to fill this gap in information, recently invented and piloted a new toolbox called the BioBio indicator set, which measures 23 different instances of biodiversity across a variety of farm types and scales in Europe. Applications were also tested in Tunisia, Ukraine, and Uganda, where they proved a feasible starting point for adaptation to the agricultural context of different countries

Comparaison de techniques d'absorption vibro-acoustiques

Cette étude propose la conception d'un banc d'essai servant à la caractérisation d'absorbeurs vibro-acoustiques. Ce banc est conçu sur la propriété d'un tube de Kundt court permettant le travail en basses fréquences (en-dessous de la première fréquence de résonance du tube). Une méthode de mesure ne (méthode à deux microphones surdéterminée) est mise en place an d'extraire les paramètres acoustiques souhaités de l'absorbeur et in ne proposer un bilan énergétique résultant et sa répartition spectrale (fréquence d'excitation et ses harmoniques)