Matching relations and the dimensional structure of social choices

The concept of a matching relation M generalizes that of an equivalence, in a case in which the domain and range of M are not necessarily identical and may be disjoint. This paper analyzes the representation of any relation R by a union of matching relations. The interpretation of such representation is that a R d — the choice of some individual or object d by some individual a requires the coincidence of at least one value of the chosen and the chooser on some relevant factor. A general discussion of matching relations is given, and various results concerning the representation are presented.     

Explicit Plancherel formula for the p-adic group GL(n)

We provide an explicit Plancherel formula for the p-adic group GL(n). We determine explicitly the Bernstein decomposition of Plancherel measure, including all numerical constants. We also prove a transfer-of-measure formula for GL(n). To cite this article: A.-M. Aubert, R. Plymen, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Spaces of lower semicontinuous set-valued maps

We give a negative answer to Problem 2 posed by R. A. McCoy in his paper [McCoy R. A.: Spaces of lower semicontinuous set-valued maps II, Math. Slovaca 60 (2010), 541–570]. Some topological properties of the space L ^?(X) introduced in [McCOY R. A.: Spaces of lower semicontinuous set-valued maps I, Math. Slovaca 60 (2010), 521–540] equipped with the Vietoris topology are also investigated.     

Comment établir des conditions nécessaires d'optimalité dans les problèmes de contrôle dont certains arguments sont déviés ?

We give a general idea to state necessary optimality conditions for problems of variational calculus or optimal control problems with deviating arguments. To cite this article: L. Samassi, R. Tahraoui, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Utilisation des modules de Drinfeld en cryptologie

We present in this Note a new and efficient public-key cryptosystem based on Drinfeld modules. The details will appear elsewhere. To cite this article: R. Gillard et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

On the singularities of analytic functions defined by L-Dirichletian elements

In this note, using the Dzrbasjan-Mandelbrojt inequality, we locate the singularities of analytic functions defined by L-Dirichletian elements. Though Dzrbasjan remarks that his inequality can be used to locate the singularities of functions defined by the Dirichlet-Taylor series, it is the convergence theory we established earlier ¦M. Blambert and M. Berland, C. R. Acad. Sci. Paris280 (1975), 263–266; M. Blambert and R. Parvatham, Ann. Inst. Fourier29 (1979), 239–262¦ that leads us exactly to determine the natural boundaries of such functions, whereas Dzrbasjan is never concerned with the convergence of such a series, as he himself states.     

Asymptotic modelling of a fluid–structure coupling in the case of a prestressed inflated orthotropic membrane shell

In this Note, we consider an inflated orthotropic linearly elastic generalized membrane shell submitted to an outer surface perturbation. We obtain the strong convergence towards the solution of a well-posed “2D” problem of the mean value in the membrane thickness 2ε of the “3D” scaled displacements, as ε approaches zero. To cite this article: R. Luce et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Nonhomogeneous Neumann problems in Orlicz–Sobolev spaces

We establish sufficient conditions for the existence of nontrivial solutions for a class of nonlinear Neumann boundary value problems involving nonhomogeneous differential operators. To cite this article: M. Mihăilescu, V. Rădulescu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Minimal singular Riemannian foliations

We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Convergence of linear finite elements for diffusion equations with measure data

We show here the convergence of the linear finite element approximate solutions of a diffusion equation to a weak solution, with weak regularity assumptions on the data. To cite this article: T. Gallouët, R. Herbin, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The centipede is determined by its Laplacian spectrum

A centipede is a graph obtained by appending a pendant vertex to each vertex of degree 2 of a path. In this Note we prove that the centipede is determined by its Laplacian spectrum. To cite this article: R. Boulet, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence

We show that the nonlinear bending theory of shells arises as a Γ-limit of three-dimensional nonlinear elasticity. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Asymptotic behaviour of certain second order integro-differential equations

The asymptotic behaviour of certain second order integro-differential equations which are more general than those equations studied in [R. P. Agarwal, J. Math. Anal. Appl.86 (1982), 471–475] and [S. R. Grace and B. S. Lalli, J. Math. Anal. Appl.76 (1980), 84–90] are discussed. It is pointed out that a defect appeared in the basic Assumption 1 made in both papers, and we avoid this defect in our discussion by using more natural conditions.     

The elliptic K3 surfaces with a maximal singular fibre

We give the defining equation of complex elliptic K3 surfaces with a maximal singular fibre. Then we study the reduction modulo p at a particularly interesting prime p. To cite this article: T. Shioda, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Functoriality of the standard resolution of the Cartesian product of a compactum and a polyhedron II

In 2003 the author has associated with every cofinite inverse system of compact Hausdorff spaces X with limit X and every simplicial complex K (possibly infinite) with geometric realization P=|K| a resolution R(X,K) of X×P, which consists of paracompact spaces. If X consists of compact polyhedra, then R(X,K) consists of spaces having the homotopy type of polyhedra. In a subsequent paper, published in 2007, the author proved that R(X,K) is a covariant functor in the first variable. In the present paper it is proved that R(X,K) is a covariant functor also in the second variable.     

On the number of rooted c-nets

W. T. Tutte (Canad. J. Math.15 (1963), 249–271) was the first person to find the number of rooted c-nets. Then, R. C. Mullin and P. J. Schellenberg found it again in another way (J. Combin. Theory4 (1968), 259–276). This note presents two simpler recursive formulae and an explicit one as a summation with all the terms positive except for at most one negative term.     

A simplified variational model for the bidimensional coupled evolution equations of a nematic liquid crystal

In Dias (C. R. Acad. Sci. Paris Sér. A. 285 (1977)) we have deduced, from Leslie's model (Arch. Rat. Mech. Anal. 28 (1968)), a weak formulation for the bidimensional coupled evolution equations of an incompressible nematic liquid crystal submitted to an homogeneous magnetic field. In this paper we prove some results about the existence, regularity and uniqueness of their solutions. This study extends the special case developed in Dias (J. Mécanique15 (1976)), where we assumed that the director field depends on time only.     

Random nonlinear Hammerstein equations

We prove existence theorems for random differential equations defined in a separable reflexive Banach space. These theorems are proved through the use of theory of random analysis established in [X. Z. Yuan, Random nonlinear mappings of monotone type, J. Math. Anal. Appl. 19] which differs from the other means, for example in [R. Kannan and H. Salehi, Random nonlinear equations and monotonic nonlinearities, J. Math. Anal. Appl. 57 (1977), 234–256; D. Kravvaritis, Existence theorems for nonlinear random equations and inequalities, J. Math. Anal. Appl. 86 (1982), 61–73; D. A. Kandilakis and N. S. Papageorgious, On the existence of solutions for random differential inclusions in a Banach space, J. Math. Anal. Appl. 126 (1987), 11–23].     

Totally geodesic Riemannian foliations with locally symmetric leaves

We prove the arithmeticity of totally geodesic Riemannian foliations, with a dense leaf, on complete finite volume Riemannian manifolds when the leaves are isometrically covered by an irreducible symmetric space of noncompact type and rank at least 2. To cite this article: R. Quiroga-Barranco, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Une borne effective sur l'écart entre le polytope de contrôle et le graphe d'un polynôme réel sur un simplexe

We provide in this Note an explicit bound on the gap between the control polytope and the graph of a real polynomial, expressed in the simplicial Bernstein basis. This generalizes known results in dimensions 1 and 2. To cite this article: R. Leroy, C. R. Acad. Sci. Paris, Ser. I 347 (2009).