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We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M, g). In other words, we establish aâ€¦ (More)

- Pierre B. A. Lecomte, Michel Rigo
- Theory of Computing Systems
- 2000

Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the lexicographic ordering.â€¦ (More)

- Pierre B. A. Lecomte, V. Yu. Ovsienko
- 1999

Let M be a smooth manifold, S the space of polynomial on fibers functions on T * M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M),â€¦ (More)

- Pierre B. A. Lecomte, Colin Dawes
- Journal of dental research
- 1987

The rate at which substances diffuse from dental plaque influences the rate of clearance of acid and bacterial toxins from plaque into saliva. The aim of this study was to compare the rates ofâ€¦ (More)

- F. Boniver, Pierre B. A. Lecomte
- 1999

Infinitesimal conformal transformations of IR n are always polynomial and finitely generated when n > 2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations overâ€¦ (More)

This article is a survey of recent work [15, 6, 7, 13] developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided byâ€¦ (More)

- Pierre B. A. Lecomte, V. Yu. Ovsienko
- 1996

We define the unique (up to normalization) symbol map from the space of linear differential operators on R n to the space of polynomial on fibers functions on T * R n , equivariant with respect toâ€¦ (More)

- Pierre B. A. Lecomte, Thomas LEUTHER, Elie ZIHINDULA
- 2012

We prove that a vector bundle Ï€ : E â†’ M is characterized by the Lie algebra generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Eulerâ€¦ (More)

- Pierre B. A. Lecomte, Michel Rigo
- Theory of Computing Systems
- 2001

Using a lexicographically ordered regular language, we show how to represent an interval of \R . We determine exactly the possible representations of any element in this interval and study theâ€¦ (More)

- Pierre B. A. Lecomte, Michel Rigo
- Inf. Comput.
- 2004

Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numerationâ€¦ (More)