Mapping fibrations.
Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices
Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density J inside the target produced by the EMD device. One approach is to develop a computational...
Matrice magique associée à un germe de courbe plane et division par l’idéal jacobien
Nous nous donnons, dans l’anneau des germes de fonctions holomorphes à l’origine de , une fonction définissant une singularité isolée et nous nous intéressons à l’équation , lorsque la fonction est donnée. Nous introduisons les multiplicités d’intersection relatives de et le long des branches de et nous étudions les solutions à l’aide de ces valuations. Grâce aux résultats ainsi démontrés, nous construisons explicitement une équation fonctionnelle vérifiée par .
Meromorphe Äquivalenzrelationen. Anwendungen, Beispiele, Ergänzungen.
Métriques sous-riemanniennes de quasi-contact : forme normale et caustique
Microlocal analysis of diffraction by a corner
Microlocal tempered inverse image and Cauchy problem.
Milnor algebras versus modular germs for unimodal hypersurface singularities.
Milnor fibration at infinity for mixed polynomials
We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.
Milnor numbers and the topology of polynomial hypersurfaces.
Minimal Characteristic Exponent of the Gauss-Manin Connection of Isolated Singular Point and Newton Polyhedron.
Minimal models of foliated algebraic surfaces
Minimal, rigid foliations by curves on
We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space for every dimension and every degree . Precisely, we construct a foliation which is induced by a homogeneous vector field of degree , has a finite singular set and all the regular leaves are dense in the whole of . Moreover, satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if is conjugate to another holomorphic foliation...
Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the case
We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail -dimensional surfaces in contact manifolds of dimension . We show that in this case minimal surfaces are projections of a special class of -dimensional surfaces...
Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case
We study minimal surfaces in sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces...
Minimaux des feuilletages algébriques de
Minorations de nombres de Milnor
Mirror symmetry and Arnold's duality.
Mixed Hodge structure of affine hypersurfaces
In this article we give an algorithm which produces a basis of the -th de Rham cohomology of the affine smooth hypersurface compatible with the mixed Hodge structure, where is a polynomial in variables and satisfies a certain regularity condition at infinity (and hence has isolated singularities). As an application we show that the notion of a Hodge cycle in regular fibers of is given in terms of the vanishing of integrals of certain polynomial -forms in over topological -cycles on...
Moderate and formal cohomology associated with constructible sheaves