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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)

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)

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)

- P. MATHONET
- 2005

The existence of a natural and projectively equivariant quan-tization in the sense of Lecomte [20] was proved recently by M. Borde-mann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields… (More)

- P. MATHONET
- 2008

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The map from the space of principal symbols to the space of differential operators is moreover required to be a linear bijection. It is known that there is in general no natural quantization procedure. However, considering manifolds… (More)

- F Boniver, P Mathonet
- 2008

The existence and uniqueness of quantizations that are equi-variant 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… (More)

- Roland Billen, Siyka Zlatanova, Pierre Mathonet, Fabien Boniver
- 2002

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)

This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present a property close to the bisymmetry property: the ordered bisymmetry property. It is proved that the class investigated contains exactly the ordered… (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 functionˆf : [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… (More)

- F Boniver, S Hansoul, P Mathonet, N Poncin
- 2008

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)