Éditeur(s) : HAL CCSD
Résumé : International audience
Here is a description of an ideal that plays an important part in the construction of projective Reed-Muller codes. The use of Eagon-Northcott complex which is a generalisation of the Koszul complex gives us a method to compute dimensions of projective Reed-Muller codes. Moreover a calculus of dimensions gives us a combinatoric identity. This communication is issued from a paper admitted in the Journal of Pure and Applied Algebra and we have adjoined a straightforward and subtle proof of the combinatoric identity given by Michel Quercia.
Actes du Colloque "Caribbean Mathematical Colloquium"
Pointe-à-Pitre, Guadeloupe

hal-00771897
https://hal.univ-antilles.fr/hal-00771897

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
With the help of differential algebras of(C,Ep)-type, we construct an algebra of generalized functions which allows us to solve a Gourmet problem with irregular data. For this problem, we perform a qualitative study when the data are Dirac functions.
ISSN: 1065-2469

hal-01545673
https://hal.archives-ouvertes.fr/hal-01545673

Éditeur(s) : HAL CCSD
Résumé : International audience
Geographic Information Systems (GIS) help addressing geographical and environmental issues by providing information about a region or a city as a set of maps (layers), each one displaying information about a given theme like roads, vegetation, tourist spots or museums for instance. By combining different layers on a region, one can associate a given area to characteristics from their related themes. Indeed, the information from two or more layers might be merged and then transformed into a new layer as defined in map "algebra". When a theme vocabulary is organized as a taxonomy with concepts linked by is-a relationships, there are different ways to annotate an area with a concept depending on the level selected into the layer taxonomy. In this paper, we present an heuristic- based approach for an optimal merging of such layers in a GIS. Our goal is to generate new layers which sum up information from several themes in a most useful way. Two optimization criteria are considered, the average size of resulting areas and the average informative value of their resulting annotation. We demonstrate the validity of the proposed solution, firstly, on a formal example, and then, on a real world application.
Proceedings of the 4th International Conference on Advanced Geographic Information Systems, Applications, and Services
Valencia, Spain

hal-00679555
https://hal.archives-ouvertes.fr/hal-00679555

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
ISSN: 1065-2469

hal-01529516
https://hal.univ-antilles.fr/hal-01529516

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Let C be a smooth curve over a Galois ring R. Let f be a function over C, and Ψ be an additive character of order p^l over R; in this paper we study the exponential sums associated to f and Ψ over C, and their L-functions. We show the rationality of the L-functions in a more general setting, then in the case of curves we express them as products of L-functions associated to polynomials over the affine line, each factor coming from a singularity of f. Finally we show that in the case of Morse functions (i.e. having only simple singularities), the degree of the L-functions are, up to sign, the same as in the case of finite fields, yielding very similar bounds for exponential sums.
ISSN: 1071-5797

hal-00551470
https://hal.archives-ouvertes.fr/hal-00551470
https://hal.archives-ouvertes.fr/hal-00551470/document
https://hal.archives-ouvertes.fr/hal-00551470/file/Charlefinal.pdf
DOI : 10.1016/j.ffa.2009.01.001