Pierre Mathonet

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The existence and uniqueness of quantizations that are equivariant with respect to conformal and projective Lie algebras of vector fields were recently obtained by Duval, Lecomte and Ovsienko. In order to do so, they computed spectra of some Casimir operators. We give an explicit formula for those spectra in the general framework of IFFT algebras classified(More)
This paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems. The common properties involved in these characterizations are “increasing monotonicity” and “stability for positive linear transformations”. Additional algebraic properties related to associativity allow to completely(More)
A unique characteristic of GIS as compared to other information systems, is their capacity to manage spatial relationships, such as connections or interrelations among objects in the geometric domain. A number of frameworks use topology as a basic mechanism to define spatial relationships. The OpenGIS consortium has adopted one of them, i.e. the(More)
The concept of system signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. We consider its extension to the continuous dependent case and give an explicit expression for this extension as a difference of weighted means of the structure function values. We then derive a formula for the computation of the coefficients of(More)
We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general N-qubit case. For this purpose, we introduce 2 parameters playing a crucial role, namely, the diversity degree and the degeneracy configuration of a symmetric state. Those parameters give rise to(More)
The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d.(More)
We prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko [6]) for the spaces Dp of differential operators transforming p-forms into functions. These results hold over a smooth manifold endowed with a flat projective structure. As an application, we classify the Vect(M)-equivariant maps from Dp to(More)
The Lovász extension of a pseudo-Boolean function f : {0, 1}n → R is defined on each simplex of the standard triangulation of [0, 1]n as the unique affine function f̂ : [0, 1]n → R that interpolates f at the n+1 vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses f . In this paper we investigate the least squares(More)