A correction to a paper of H. King.
A geometric point of view on mean-variance models
This paper deals with the mathematics of the Markowitz theory of portfolio management. Let E and V be two homogeneous functions defined on ℝⁿ, the first linear, the other positive definite quadratic. Furthermore let Δ be a simplex contained in ℝⁿ (the set of admissible portfolios), for example Δ : x₁+ ... + xₙ = 1, . Our goal is to investigate the properties of the restricted mappings (V,E):Δ → ℝ² (the so called Markowitz mappings) and to classify them. We introduce the notion of a generic model...
A gradient inequality at infinity for tame functions.
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
A Note on Right-Equivalence of Map-Germs.
A Note on the Order of Determination of a Finitely Determined Germ.
A Splitting Theorem for Maps Into IR2 .
A Sufflcient Condition for a Critical Point of a Functional to be a Minimum and Its Application to Plateau' s Problem.
A theorem on the escape from the space of hyperbolic polynomials.
Affinely invariant symmetry sets
The classical medial axis and symmetry set of a smooth simple plane curve M, depending as they do on circles bitangent to M, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the 'centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane curve, which...
Algebras Q (f) Determine the Topological Types of Generic Map-Germs.
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
An arithmetic characterisation of the symmetric monodromy groups of singularities.
An extension to fields of positive characteristic of Mather's construction of the Thom-Boardman sequence
Applications des faisceaux analytiques semi-cohérents aux fonctions différentiables
Nous appliquons les résultats d’un article précédent au domaine des fonctions différentiables. Nous obtenons en particulier des théorèmes de division et des théorèmes de fonctions composées.
Bernstein-Sato Polynomials and Spectral Numbers
In this paper we will describe a set of roots of the Bernstein-Sato polynomial associated to a germ of complex analytic function in several variables, with an isolated critical point at the origin, that may be obtained by only knowing the spectral numbers of the germ. This will also give us a set of common roots of the Bernstein-Sato polynomials associated to the members of a -constant family of germs of functions. An example will show that this set may sometimes consist of all common roots.
Bifurcations in symplectic space
In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.
Bifurcations of affine invariants for one-parameter family of generic convex plane curves
We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.
Bifurcations of generic one parameter families of functions on foliated manifolds.
Bifurkation von Minimalflächen und elementare Katastrophen.
Catastrophe models and the expansion method: A review of issues and an application to the econometric modeling of economic growth.