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Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures

Julian Ławrynowicz, Alain Mignot, Loucas Papaloucas, Claude Surry (1996)

Banach Center Publications

A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.

Modified Nash triviality of a family of zero-sets of real polynomial mappings

Toshizumi Fukui, Satoshi Koike, Masahiro Shiota (1998)

Annales de l'institut Fourier

In this paper we introduce the notion of modified Nash triviality for a family of zero sets of real polynomial map-germs as a desirable one. We first give a Nash isotopy lemma which is a useful tool to show triviality.Then, using it, we prove two types of modified Nash triviality theorem and a finite classification theorem for this triviality. These theorems strengthen similar topological results.

Modular classes of Q-manifolds: a review and some applications

Andrew James Bruce (2017)

Archivum Mathematicum

A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including L -algebroids and higher Poisson manifolds.

Modular vector fields and Batalin-Vilkovisky algebras

Yvette Kosmann-Schwarzbach (2000)

Banach Center Publications

We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose d P -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the Gerstenhaber...

Modules pour les familles de courbes planes

Jean-Paul Dufour (1989)

Annales de l'institut Fourier

L’étude des familles de courbes plane différentiables se ramène a celle des diagrammes f S σ 2 S est une surface, f et σ étant différentiables. Dans la classification de ces diagrammes à équivalence près il apparaît trois types de modules: des modules locaux attachés à chaque fronce de σ , des modules semi-locaux attachés à la superposition en un même point de plusieurs situations locales, des modules globaux attachés aux “courbes de contact” le long desquelles certaines courbes sont tangentes. Nous explicitons...

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