Key Polynomials

The notion of key polynomials was first introduced in 1936 by S. Maclane in the case of discrete rank 1 valuations. . Let K -> L be a field extension and {\nu} a valuation of K. The original motivation for introducing key polynomials was the problem of describing all the extensions {\mu} of {\nu} to L. Take a valuation {\mu} of L extending the valuation {\nu}. In the case when {\nu} is discrete of rank 1 and L is a simple algebraic extension of K Maclane introduced the notions of key polynomials for {\mu} and augmented valuations and proved that {\mu} is obtained as a limit of a family of augmented valuations on the polynomial ring K[x]. In a series of papers, M. Vaqui\'e generalized MacLane's notion of key polynomials to the case of arbitrary valuations {\nu} (that is, valuations which are not necessarily discrete of rank 1). In the paper Valuations in algebraic field extensions, published in the Journal of Algebra in 2007, F.J. Herrera Govantes, M.A. Olalla Acosta and M. Spivakovsky develop their own notion of key polynomials for extensions (K, {\nu}) -> (L, {\mu}) of valued fields, where {\nu} is of archimedian rank 1 (not necessarily discrete) and give an explicit description of the limit key polynomials. Our purpose in this paper is to clarify the relationship between the two notions of key polynomials already developed by vaqui\'e and by F.J. Herrera Govantes, M.A. Olalla Acosta and M. Spivakovsky.Comment: arXiv admin note: text overlap with arXiv:math/0605193 by different author

Simple but Stronger UO, Double but Weaker UNMe Bonds: The Tale Told by Cp2UO and Cp2UNR

The free energies of reaction and the activation energies are calculated, with DFT (B3PW91) and small RECP (relativistic core potential) for uranium, for the reaction of Cp2UNMe and Cp2UO with MeCCMe and H3Si-Cl that yields the corresponding addition products. CAS(2,7) and DFT calculations on Cp2UO and Cp2UNMe give similar results, which validates the use of DFT calculations in these cases. The calculated results mirror the experimental reaction of [1,2,4-(CMe3)3C5H2]2UNMe with dimethylacetylene and [1,2,4-(CMe3)3C5H2]2UO with Me3SiCl. The net reactions are controlled by the change in free energy between the products and reactants, not by the activation energies, and therefore by the nature of the UO and UNMe bonds in the initial and final states. A NBO analysis indicates that the U-O interaction in Cp2UO is composed of a single U-O bond with three lone pairs of electrons localized on oxygen, leading to a polarized U-O fragment. In contrast, the U-NMe interaction in Cp2UNMe is composed of a and component and a lone pairof electrons localized on the nitrogen, resulting in a less polarized UNMe fragment, in accord with the lower electronegativity of NMe relative to O. The strongly polarized U(+)-O(-) bond is calculated to be about 70 kcal mol-1 stronger than the less polarized U=NMe bond

Essai d'hyperoxygenation des mouts sur cepages locaux en Alsace

National audienc

A Qualitative Theory of Motion Based on Spatio-Temporal Primitives

This paper presents a formal theory for reasoning about motion of spatial entities, in a qualitative framework. Taking over a theory intended for spatial entities, we enrich it to achieve a theory whose intended models are spatio-temporal entities, an idea sometimes proposed by philosophers or AI authors but never fully exploited. We show what kind of properties usually assumed as desirable parts of any space-time theory are recovered from our model, thus giving a sound theoretical basis for a natural, qualitative representation of motion. 1 INTRODUCTION This paper presents a theory for representing and reasoning about motion in a qualitative framework. A lot of work has been devoted to the representation of space in the past few years, as spatial concepts pervades many domains of AI. Part of these works have focused on the building of theories for reasoning about incomplete and/or imprecise information as such theories would be more easily exploited than the traditional quantitative ..