Plaine du Forez

Neuf communes de part et d’autre de la Loire ont été choisies comme zone-test autour de Feurs (importante occupation protohistorique et gallo-romaine). En 1992, une campagne de prospections a été menée pendant le mois d’octobre, après une période d’étude topographique, toponymique et un dépouillement bibliographique. Chaque commune a fait l’objet d’une carte avec les zones prospectables et les zones prospectées. 33 nouveaux gisements ont été repérés (146 au total)

Plaine du Forez

Les prospections menées sur la plaine du Forez se présentent comme la suite de l’étude entamée en 1990. Neuf communes avaient été choisies comme zone test autour de Feurs, afin de mieux appréhender le peuplement de cette plaine. Située de part et d’autre de la Loire, ce territoire avait l’avantage de traverser des secteurs géographiques différents, et plus ou moins bien prospectés selon les endroits. Pour toutes les périodes des questions d’ordre historique ont été posées. Pour la Protohistoi..

Feurs – Rue Motton, rue Gambetta, rue Michelet, rue Jules-Ferry

Deux interventions se sont déroulées chez des particuliers : des sondages avant la construction d’une maison individuelle, rue Michelet (responsable : M.-O. Lavendhomme) ; une surveillance de terrassements pour la construction de garages, rue Jules-Ferry (responsable : É. Plassot). À cela, s’ajoutent diverses observations effectuées lors du suivi de travaux de réaménagement de la voirie. Ceux-ci s’inscrivent dans un programme de restructuration de la circulation en centre-ville, engagé par l..

Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

Extension from memory kits to inductively derived views

Inductive Game Theory (IGT) was developed to study the emergence of the subjective views of individuals in a social situation. In this paper we give an explicit extension process (EP) to go from a memory kit to an inductively derived view (i.d.view). We address the multiplicity problem of i.d.views by requiring a stronger link between memory threads used in the EP. We call this process a linking EP. We give a necessary and sufficient condition on the memory kit for the set of i.d.views obtained by linking EP’s to be non-empty. We give another condition for the set of i.d.views obtained to be finite. Sufficient conditions are also given directly on the objective view

Relative commutator theory in varieties of omega-groups

We introduce a new notion of commutator which depends on a choice of subvariety in any variety of omega-groups. We prove that this notion encompasses Higgins's commutator, Froehlich's central extensions and the Peiffer commutator of precrossed modules.Comment: 16 page

Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics

International audienceWe develop semantically-oriented calculi for the cube of non-normal modal logics and some deontic extensions. The calculi manipulate hypersequents and have a simple semantic interpretation. Their main feature is that they allow for direct countermodel extraction. Moreover they provide an optimal decision procedure for the respective logics. They also enjoy standard proof-theoretical properties, such as a syntactical proof of cut-admissibility

Change Actions: Models of Generalised Differentiation

Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model for (higher-order) generalised differentiation. Change action models naturally arise from many geometric and computational settings, such as (generalised) cartesian differential categories, group models of discrete calculus, and Kleene algebra of regular expressions. We show how to build canonical change action models on arbitrary cartesian categories, reminiscent of the F\`aa di Bruno construction

`Iconoclastic', Categorical Quantum Gravity

This is a two-part, `2-in-1' paper. In Part I, the introductory talk at `Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international theoretical physics conference is presented in paper form (without references). In Part II, the more technical talk, originally titled ``Abstract Differential Geometric Excursion to Classical and Quantum Gravity'', is presented in paper form (with citations). The two parts are closely entwined, as Part I makes general motivating remarks for Part II.Comment: 34 pages, in paper form 2 talks given at ``Glafka--2004: Iconoclastic Approaches to Quantum Gravity'' international theoretical physics conference, Athens, Greece (summer 2004

Relative Commutator Theory in Semi-Abelian Categories

Basing ourselves on the concept of double central extension from categorical Galois theory, we study a notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian category A. This commutator characterises Janelidze and Kelly's B-central extensions; when the subcategory B is determined by the abelian objects in A, it coincides with Huq's commutator; and when the category A is a variety of omega-groups, it coincides with the relative commutator introduced by the first author.Comment: 22 page