Pierre Mathonet

Operational Families of Entanglement Classes for Symmetric N-Qubit States

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 a simple method of identifying operational families of SLOCC entanglement classes of all symmetric N-qubit states, where the number of families grows as the partition function of the number of qubits.

Comparison of some modules of the Lie algebra of vector fields

Abstract The Lie algebra of vector fields of a smooth manifold M acts by Lie derivatives on the space D k p of differential operators of order ≤ p on the fields of densities of degree k of M. If dim M ≥ 2 and p ≥ 3, the dimension of the space of linear equivariant maps from D k p into D l p is shown to be 0, 1 or 2 according to whether (k, l) belongs to 0, 1 or 2 of the lines of R 2 of equations k = 0,k = − 1, k = l and k + l + 1 = 0. This answers a question of C. Duval and V. Ovsienko who have determined these spaces for p ≤ 2[2].

The Dimensional Model: A Framework to Distinguish Spatial Relationships

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 9-intersection model. In this paper, a new framework for representing spatial relationships — the Dimensional model — is introduced. The model was first developed for convex spatial objects and is now extended to topological n-manifolds. It is based on two major concepts, i.e. the dimensional elements of spatial objects and the dimensional relationships, i.e. the relationships existing between dimensional elements. The model addresses a substantial group of spatial relationships and provides a flexible framework to consider either generalised or specialised types of associations.

Characterization of some aggregation functions stable for positive linear transformations

Abstract 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 specify the functions.

On signature-based expressions of system reliability

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. case, we show that, at any time, this representation still holds true for every coherent system if and only if the component states are exchangeable. We also discuss conditions for obtaining an alternative representation of the system reliability in which the signature is replaced by its non-i.i.d. extension. Finally, we discuss conditions for the system reliability to have both representations.

EQUIVARIANT SYMBOL CALCULUS FOR DIFFERENTIAL OPERATORS ACTING ON FORMS

AbstractWe prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko) for the spaces

Natural and Projectively Equivariant Quantizations by means of Cartan Connections

\mathcal{D}_p

Intertwining operators between some spaces of differential operators on a manifold

of differential operators transforming p-forms into functions, over