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The Mousterian level of the Doline of Cantalouette 2, with a mean age of 60 000 years, is remarkable for its richness, composition and recurrent structuring of activities in space (Bourguignon et al. 2008). It also delivers a range of lithic tools used in percussion tasks. In addition to a large range of knapping hammers (on quartz pebbles, flakes or flint cores), massive flint flakes have also been used with percussion gestures for working perishable materials such as animal carcasses and plants. We will focus our present article exclusively on this last type of use. The lithic production activities of this Late Mousterian mainly involved an algorithmic knapping system, based on recurrent unidirectional series and obtained according to sub-parallel fracture planes following one or more surfaces. Thick flakes, often with lateral asymmetry, were obtained from one or more circumscribed percussion planes (opposite or perpendicular), which are very rarely prepared. More rarely, a preferential Levallois knapping system, oriented towards export of the products, was also implemented. At some distance from the knapping station the main production was made almost exclusively for immediate use with or without a preparation of the active and handling parts by retouching, (Bourguignon et al. 2008). From this lithic production, it was made a selection of massive flakes easily handled with bare hands. These blanks often came from the first stages of the operating chain (cortical) and were used in percussion tasks. On the basis of a macroscopic selection of the - often unretouched - cutting edges with stigmas of crushing, micro-flaking or scarring, a functional analysis was carried out according to the analytical methodology developed by Semenov (1964). As the tools were very large items, we produced replicas of the working edges on acetate for additional analysis with microscope. Two types of percussion activities were registered, one focused on butchering tasks and the other on woodworking. For the butchering activities, these large, massive flakes were used as cleavers, chopping knives or butchering blades. On the edges of these tools, large scars are documented, resulting from striking the bones during the disarticulation or chopping of animal parts. Hard/semi-hard vegetal and woody plant materials were also worked by percussion gestures, mainly in order to slim them. Some very large lithic tools suggest a two-handed grip. In those cases, only one of the edges is used. On the smaller items, which can be held with one hand, the number of active parts is greater (at least two). These active parts are often denticulate (presenting a number of notches, retouched or not). The use-wear polishes concentrate on these areas. In some cases, these denticulations were prepared previously to use. For other tools, denticulations may also be the consequence of the impact on the material during the percussion tasks. These two registered activities will, therefore, be presented here, detailing and illustrating the stigmas and use-wear polishes relating to each of them. [ABSTRACT FROM AUTHOR]

Abstract: In this article we verify Dufloʼs conjecture for with respect to a Borel subgroup. It turns out that the non-standard notion weakly proper (faiblement propre) in the formulation of Dufloʼs conjecture is more reasonable than the standard notions proper and proper over image. [Copyright &y& Elsevier]

Abstract: In this Note, we determine the minimum Hellinger distance estimate of an ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process. The estimate minimizes the Hellinger distance between the probability density function of the innovation of the process and a parameterized random function. Under some assumptions, we establish the asymptotic properties of this estimate. [Copyright &y& Elsevier]

Abstract: We study -estimates for on pseudoconvex domains Ω relatively compact in a complete Kähler manifold with positive holomorphic bisectional curvature. We define a function on -smooth pseudoconvex domains. On these domains, we prove that there exists a neighborhood of ∂Ω on which . A generalization of this property allows us, among others, to prove -estimates for on pseudoconvex domains Ω with a defining plurisubharmonic function and a positive inner reach. [Copyright &y& Elsevier]

Abstract: The ridgelet transform is extended to Wiener functionals. Even if the reconstruction property is not satisfied, we still approximate a Wiener functional with the help of its transform and we give an application to its regularity. [Copyright &y& Elsevier]

Abstract: In this Note, we introduce the local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space. Under some general conditions, we establish the pointwise and uniform almost complete convergences with rates of this estimator. Moreover, as an application, we use the obtained results to derive some asymptotic properties for the local linear estimator of the conditional mode. [ABSTRACT FROM AUTHOR]

Dans cet article nous étudions trois notes de M. Fréchet sur les opérations linéaires (publiées entre 1904 et 1906) et leur rôle dans l’émergence de l’analyse fonctionnelle au début du XXème siècle. Dans un premier temps nous mettons en évidence les processus de sélection, d’extraction et de réinterprétation mis en œuvre par Fréchet à partir de matériaux publiés antérieurement. A partir de cette analyse nous nous attachons à montrer comment la progression vers une vision plus générale met en jeu des éléments structurels fondamentaux dans la constitution d’un champ nouveau des mathématiques. Notre étude permet finalement de préciser le concept de structure dans son rôle central dans l’émergence de l’analyse fonctionnelle. [ABSTRACT FROM AUTHOR]

This article focuses on multidisciplinary optimization in situations in which the different criteria that account for the various disciplines are functionals of distributed solutions of partial-differential equations. In the case of two disciplines, we propose a strategy in which the optimization process is carried out in two phases: (a) a cooperative-optimization phase throughout which both criteria improve at each iteration, and (b) an optional competitive-optimization phase by a Nash game associated with an adapted split of variables. [ABSTRACT FROM AUTHOR]

Abstract: Ground stone tools are lithic tools made on coarse blanks that are not included in the chipped or polished stone studies. During the study of a ground stone tools collection coming from the Campaniform site of Beg ar Loued (Molène island, Finistère, France), the techno-functional unit (TFU) analysis as been adapted to these objects. A TFU is a part of a tool that is technologically independent, having his own part in this tool''s overall functioning. The application of this method to ground stone tools needed some adaptations to their characteristics. The aim is to obtain a high level technological analysis for these tools, succeeding to express functional hypothesis. Two concrete examples from Beg ar Loued''s collection illustrate the TFU analysis method''s application to ground stone tools. This method has the advantage to organize the progress of each piece''s analysis. The TFU analysis helps to understand the multifunctional tools by considering each function as a full tool. This allows us to talk about function''s hierarchisation and their adaptation to blanks. We also obtain some informations about blank''s selection. These many and varied results make the TFU analysis essential for ground stone tool''s technological and functional analysis. [Copyright &y& Elsevier]

Abstract: In 2003 and 2004, two series of projectile experiments were organized by P. Cattelain and ourselves at the CEDARC/Musée du Malgré-Tout (Treignes, Belgium). The experiments involved the use of two male ox calves and two female fallow deers as targets for bow and spearthrower shooting. Our main focus was a functional analysis of the antler projectile tips from the Upper Magdalenian layer of the Isturitz cave site (Pyrénées-Atlantiques, France). The study of the impact traces on the bones of the target animals was also included in the project; its results are presented here. The observation of these 127 traces led us to reconsider the nomenclature suggested by P. Morel, and to distinguish between three major traces: notches, punctures and perforations. Correlations appear between the nature of the trace and the shape of the bone (e.g., scapulae strongly associated to perforations), and the bone''s mineral content: compared to adult long bones, immature long bones are much more easily perforated by projectile points, which usually remain firmly caught in them. However, our results do not show a clear distinction between the impact traces left by the bow and by the spearthrower. [Copyright &y& Elsevier]

Abstract: In this Note we introduce a general approach to construct structural testing procedures in regression on functional variables. In the case of multivariate explanatory variables a well-known method consists in a comparison between a nonparametric estimator and a particular one. We adapt this approach to the case of functional explanatory variables. We give the asymptotic law of the proposed test statistic. The general approach used allows us to cover a large scope of possible applications as tests for no-effect, tests for linearity, …. To cite this article: L. Delsol, C. R. Acad. Sci. Paris, Ser. I 346 (2008). [Copyright &y& Elsevier]

Abstract: We generalize Casselman''s pairing to p-adic reductive symmetric spaces and study the asymptotic behaviour of certain generalized coefficients. We also prove an analogue of a lemma due to Langlands which allows us to prove a disjunction result for the Cartan decomposition of the p-adic reductive symmetric spaces. [Copyright &y& Elsevier]

Abstract: This Note focuses on an automatical choice of the functional parameter introduced throughout the single functional index model when one regresses a real r.v. on a functional r.v. (i.e. valued in an infinite-dimensional space). This Note aims to prove that a cross-validation-based method leads to an asymptotic optimal choice of the functional index. In addition, one states that such a choice for the functional index is a consistent estimator. To cite this article: A. Ait-Saïdi et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). [Copyright &y& Elsevier]

Abstract: We give some approximations of the local time process at level x of the real Brownian motion . We prove that and converge in the ucp sense to , as . We show that goes to in as , and that the rate of convergence is of order , for any . To cite this article: B.B. Bergery, P. Vallois, C. R. Acad. Sci. Paris, Ser. I 345 (2007). [Copyright &y& Elsevier]

Abstract: On a compact Riemannian manifold , a long-standing question is: Does the set of the solutions of the Yamabe equation compact in ? There are three cases in the Yamabe problem (see Aubin [T. Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, New York, 1998]) according to the sign of the inf of the Yamabe functional. We prove the compactness of the set of the solutions of the Yamabe equation (except on the sphere) in the positive case, the only case which makes difficulties. [Copyright &y& Elsevier]

Abstract: We give a result of uniqueness for the three-dimensional Navier–Stokes system; the class of uniqueness that we consider is where is the space of pointwise multipliers from to . We also give a very simple proof to the uniqueness of solutions in . To cite this article: F. Marchand, M. Paicu, C. R. Acad. Sci. Paris, Ser. I 344 (2007). [Copyright &y& Elsevier]

Abstract: Given an affine scheme X with an action of a reductive group G and a G-linearized coherent sheaf , we construct the “invariant Quot scheme” that parametrizes the quotients of whose space of global sections is a direct sum of simple G-modules with fixed finite multiplicities. Then we determine the invariant Quot scheme in a simple situation, where X is the cone of primitive vectors of a simple G-module and is the free sheaf on X generated by another simple G-module. This invariant Quot scheme has only one point, that is reduced in most of the cases. The only cases where it is not reduced occur when X is the cone of primitive vectors of a quadratic vector space V of odd dimension, under the action of . [Copyright &y& Elsevier]

Abstract: We prove a Hilbert''s Seventeenth problem theorem and an approximation theorem in the style of Greenberg in the case of discrete D-valued fields in the sense of T. Scanlon. To cite this article: N. Guzy, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: In this Note we present a formal scaling method that allows for the deduction from three-dimensional linearized elasticity of the equations of shearable structures such as Reissner–Mindlin''s equations for plates and Timoshenko''s equations for rods, as well as other models of thin structures. This method is based on the requirement that a scaled energy functional possibly including second-gradient terms stay bounded in the limit of vanishing ‘thinness’. To cite this article: B. Miara, P. Podio-Guidugli, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: We define new classes of sets with large intersection, which generalize those introduced by K. Falconer. These classes contain the sets which are defined using homogeneous and heterogeneous ubiquitous systems. Such sets play an important role in Diophantine approximation and in multifractal analysis. To cite this article: A. Durand, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: We define the functor category , associated to -vector spaces equipped with a quadratic form. We state results about simple objects of this category, including a classification of the simple objects which are non zero on the quadratic spaces of dimension two. To cite this article: C. Vespa, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: We consider a mixed finite element method for the contact problem in elasticity that furnishes approximated fields (displacements and constraints) satisfying the sign conditions of the continuous problem. We prove that the method verifies similar a priori error estimates as the standard method. To cite this article: P. Hild, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: Recently R. Danchin showed the existence and uniqueness for an inhomogenous fluid in the homogeneous Besov space , under the condition that is small in if in if In this Note, one shows that the condition is sufficient to have the existence and uniqueness. To cite this article: H. Abidi, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Abstract: From differential analysis for the identification of biomarkers, to functional analysis for the evidencing of new therapeutic targets, proteomics brings new comprehensive information for a better understanding of the molecular basis of oncology and new perspectives for the clinic. However the major limitation of proteomic investigations and more generally of post-genomic approaches remains the molecular and cellular complexity of biological systems. This will be illustrated with the case of breast cancer. [Copyright &y& Elsevier]

Abstract: In this Note, we give some results on the -error estimates and convergence in the Sobolev space for the interpolation by thin splines under tension. To cite this article: A. Bouhamidi, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Abstract: In this Note, following ideas first initiated by Fantappiè ([L. Fantappiè, Sur les méthodes nouvelles d''intégration des équations aux dérivées partielles au moyen des fonctionnelles analytiques, in : La théorie des équations aux dérivées partielles, vol. 81, Coll. Int. CNRS, Nancy, 9–15 avril 1956. ], [F. Pellegrino, Problèmes concrets d''analyse fonctionnelle, P. Levy (Ed.), Gauthier-Villars, Paris, 1951, pp. 357–484. ]), we make a link between Cauchy problems, analytic functionals and functional calculus. In particular, using classical representation formulas from complex analysis, we obtain an integral representation formula for solutions to complex Cauchy problems. Moreover, recent developments in complex convex analysis of Andersson–Passare–Sigurdsson allow us to obtain a domain of definition of the solution if Cauchy data are defined in a -convex domain. To cite this article: S. Rigat, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Abstract: We prove an almost sharp Superposition Theorem for a wide class of Besov spaces. Indeed any function which belongs locally to , and vanishes at 0, acts by left composition in . The conditions on the parameters are the following: , and . To cite this article: G. Bourdaud, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Abstract: A possible relevant meaning of Hilbert’s program is the following one: “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs (that use Third Excluded Middle and Choice) about abstract objects, as constructive proofs about constructive versions of these objects. If this program is fulfilled we are able “at the end of the tale” to extract constructive proofs of concrete results from classical abstract proofs of these results. Dynamical algebraic structures or (this is more or less the same thing) geometric theories seem to be a good tool for doing this job. In this setting, classical abstract objects are interpreted through incomplete concrete specifications of these objects. The structure of axioms in geometric theories gives rise in a natural way to distributive lattices and pointfree topological spaces. Abstract objects correspond to classical points of these pointfree spaces. We shall insist on the Zariski spectrum of distributive lattices and commutative rings and give a constructive interpretation of the Krull dimension. We underline the fact that many abstract objects in classical mathematics can be viewed as points of spectral spaces corresponding to distributive lattices whose definition is concrete and natural. Two important facts are to be stressed. First, abstract proofs about points of these pointfree spaces can very often (always?) be reread as constructive proofs about constructible subsets of these spaces. Second, function spaces on these pointfree spaces are often explicitly used in elegant abstract theories. The structure of these function spaces is fully constructive: indeed by the compactness theorem, “all is finite”. The constructive rereading of the abstract proofs is in this setting is nothing but the simple constatation that abstract proofs use correctly (geometric) axioms. [Copyright &y& Elsevier]

Abstract: It is shown that the limits of Faedo–Galerkin approximations of the Navier–Stokes equations in the three-dimensional torus are suitable weak solutions to the Navier–Stokes equations provided they are constructed using finite-dimensional spaces having a discrete commutator property and satisfying a proper inf–sup condition. Low order mixed finite element spaces appear to be acceptable for this purpose. This question was open since the notion of suitable solution was introduced. To cite this article: J.-L. Guermond, C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]

Abstract: Consider an equivariant extension of graded separable G-algebras which admits a completely linear positive, grading preserving cross section (not necessary equivariant) of norm 1. We denote an amenable topological transformation group in the sense of Anantharaman-Delaroche. We establish an isomorphism concerning the Kasparov equivariant bifunctor . This isomorphism in K-theory, allows one to extend the half-exactness from the case of the proper algebras (which is analogue to the one obtained by Skandalis in the non-equivariant case) to the case of amenable actions. In particular, we will place ourselves in a significant case, that of hyperbolic displacements of the Poincaré–Lobatschevsky geometry on the unit disc. To cite this article: D. El Morsli, C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]

Abstract: A case of natural decomposition of plethysm is studied. We work within the category of functors between vector spaces over a prime field . The symmetric power of a functor B is shown to split when B takes p-boolean algebras values—these are algebras whose product satisfies . The injective envelope of the identity functor takes such values. This is applied to functor cohomology computations, which are relevant to the study of the cohomology of Eilenberg–Mac Lane spaces. [Copyright &y& Elsevier]

Abstract: Let m be an integer ⩾3, set for , and consider a badly approximable vector . Fix , and . We construct a sequence of Hamiltonian functions of , which converges to ℏ when , such that for each N the system generated by possesses a -dimensional hyperbolic invariant torus with fixed frequency vector , which admits a homoclinic point with splitting matrix of the form , with , where and . To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: The uncertainty principle states that a nonzero function and its Fourier transform cannot be both sharply localized. It is well known that the support and the spectrum of a function cannot both have finite measure. In Shubin et al. [Geom. Funct. Anal. 8 (1998) 932–964], it is shown that they cannot be contained in ɛ-thin sets E and . We give here other examples of sets E and having this property. The thinness of the sets is expressed in terms of a dyadic decomposition of the space, which is related to the functions on . These sets are not ɛ-thin in general. We prove that the pairs of sets we consider are strongly annihilating in the sense of Havin and Jöricke. To cite this article: B. Demange, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: Using some properties of the Hardy spaces, we give a regularity result on the advection term of the shallow-water equations and we show a bound holding up to the boundary on the water height with Dirichlet boundary conditions. To cite this article: F. Flori, P. Orenga, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: We consider bounded linear operators defined on real normed spaces, and with range in quaternionic spaces. We study the norms of the quaternionic extensions of such operators. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: We call a finite-dimensional complex Lie algebra strongly rigid if its universal enveloping algebra is rigid as an associative algebra, i.e., every formal associative deformation is equivalent to the trivial deformation. In quantum group theory this phenomenon is well known to be the case for all complex semisimple Lie algebras. We show that a strongly rigid Lie algebra, over a field of characteristic 0, has to be rigid as Lie algebra, and that in addition its second scalar cohomology group has to vanish (which excludes nilpotent Lie algebras of dimension greater or equal than two). Moreover, using Kontsevitch''s theory of deformation quantization we show that every polynomial deformation of the linear Poisson structure on which induces a nonzero cohomology class of a complex Lie algebra leads to a nontrivial deformation of . Hence every Poisson structure on a vector space which is zero at some point and whose linear part is a strongly rigid Lie algebra is therefore formally linearizable in the sense of A. Weinstein. Finally we provide examples of rigid Lie algebras which are not strongly rigid, and give a classification of all strongly rigid Lie algebras up to dimension 6. [Copyright &y& Elsevier]

Abstract: We define a point evaluation for transfer operators of multiscale causal dissipative systems. We associate to such a system a de Branges Rovnyak space, which serves as the state space of a coisometric realization. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: In this Note we give an elementary proof of a well-known identity in law involving quadratic functionals of the Brownian bridge. To cite this article: J.-R. Pycke, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: Let us assume that , , and . If f and g are functions in the Besov space , such that g is real valued and such that , then the composed function belongs to . To cite this article: G. Bourdaud, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: We generalise the Beurling–Nyman criterion, already known for the Riemann ζ function, to a larger class of Dirichlet series. We link the density of some subspace of functions in and the localization of the zeros of a Dirichlet series. To do so, we use the structure of the Hardy space of the half-plane. To cite this article: A. de Roton, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Let Lω2(R) be a weighted space with weight ω. In this paper we show that for every bounded operator T on Lω2(R) which commutes with translations, and for every a∈Iω, there exists a function νa∈L∞(R) such that Here (g)a denotes the function x↠g(x)eax for g∈Lω2(R) and Iω=[lnRω-,lnRω+], where Rω+ is the spectral radius of the bilateral shift S :f(x)↠f(x-1) on Lω2(R), while 1/Rω- is the spectral radius of S-1. Moreover there exists a constant Cω depending on ω such that ǁνaǁ∞⩽CωǁTǁ for every a∈Iω. If Rω-, there exists a bounded holomorphic function ν on Åω:={z∈C∣Imz∈&Iring;ω}, such that Tf=ν&fcirc;, ∀f∈D(R) and ǁνǁ∞⩽CωǁTǁ, where Tf(a+ix)=(Tf)a(x) for a∈&Iring;ω. [Copyright &y& Elsevier]

Let Ω be a strongly Lipschitz domain of Rn (n⩾2). We give endpoint versions of div–curl lemmata on Ω, for a given function f on Ω whose gradient belongs to a Hardy space on Ω. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]

We characterize complete Hausdorff locally convex solid lattices (E,τ) satisfying the following property: for all operators S,T :E→E such that 0⩽S⩽T and T precompact, the operator S2 is precompact. To cite this article: B. Aqzzouz, R. Nouira, C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]

In this paper, we study a convection-diffusion model with respect to a vector field having log-Lipschitz regularity. More precisely, we are interested in the viscous repartition of the mass for the solutions of the corresponding equation. We prove that mass is essentially concentrated around the image, through the flow, of the initial support. This allows us, for non-regular bidimensional vortex patches, to prove the global Lp convergence of the Navier–Stokes vorticity ων to the Eulerian vorticity ω, with p>1. To cite this article: T. Hmidi, C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]

We consider the solution X=(Xt)t⩾0 of a time-inhomogeneous stochastic differential equation and the exit time τ by (t,Xt)t⩾0 of the time–space domain D. We prove the differentiability of expectations of functionals of X stopped at τ, with respect to the domain D: these results extend those in the literature, known in particular by the analysts for the issues of shape optimization. However from the probabilistic point of view, this is not standard. To cite this article: C. Costantini et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]

Abstract: We model propagation of electromagnetic waves in a medium, which is inhomogeneous with a rough layer, and which hides an object. We first get an effective medium, and then we solve the problem by integral equations. [Copyright &y& Elsevier]