La valeur d'un entier classique en \lambda\mu-calcul

In this paper, we present three methods to give the value of a classical integer in -calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the corresponding Church integer. The third method is the M. Parigot's method which uses the J.L. Krivine's storage operators.

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Re?u le 4 Septembre 1995     

Ideaux a droite maximaux d'un anneau

Sans résumé     

Polynomes a valeurs entieres sur un anneau de pseudovaluation

We study the ring of integral valued polynomials over a pseudovaluation domain A. We entirely determine the set of prime ideals above the maximal ideal M of A: if M is a principal ideal in the valuation domain V associated with A and if its residue field is finite, then this set is in bijection with a topologically complete ring, as in the Noetherian case; if M is principal but of infinite residue field in V, then this set is finite; at last, if M is not principal, then the ring of integral valued polynomials is included in V[X] and has the same set of prime ideals above M.     

Étalement en couche mince d'un jet liquide cylindrique vertical sur un plan horizontal

Résumé Quand un jet liquide cylindrique vertical tombe sur une plaque plane horizontale, il s'étale en général sur celle-ci en un écoulement en film mince limité par un ressaut circulaire, au delà duquel, le film a une épaisseur plus grande. Une étude théorique est faite aussi bien en zone torrentielle qu'en zone fluviale et la position du ressaut est déterminée; ces résultats sont comparés aux courbes expérimentales et l'évolution du profil des vitesses est déterminée dans la zone fluviale par anémométrie laser.

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Conclusion Cette étude nous a permis de mettre en évidence une concordance acceptable entre le profil réel et le profil semi-parabolique des vitesses dans la zone fluviale dans le cas de nos conditions expérimentales [11]. D'autres conditions, ne permettant pas le renouvellement constant du liquide de la surface libre, auraient conduit certainement à un autre type de profil [12]. Par ailleurs le calcul théorique associé à ce profil nous a permis de prévoir la position du ressaut avec une précision acceptable. Enfin, la structure du ressaut relatif à ce type d'écoulement a pu être précisée.When a cylindrical vertical liquid jet falls on an horizontal flat plate it spreads out generally in a thin layer bounded by a circular hydraulic jump outside which the layer has a much greater depth. The theoretical study is done for the supercritical and subcritical flows and the hydraulic jump is located. The relations obtained are compared with experimental results and the evolution of the velocity profil is determined in the subcritical flow by laser anemometry.

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Cette recherche a fait l'objet d'un contrat ONRS (Organisme National de la Recherche Scientifique Algérien) No. 76 AA 01/1.     

Sur les petites oscillations planes d'un liquide dans un container symétrique en apesanteur

Résumé L'auteur étudie le problème bidimensionnel des oscillations d'un liquide dans un container symétrique en apesanteur. II donne l'équation fonctionnelle du mouvement et prouve l'existence des fréquences propres du liquide sous des conditions convenables portant sur l'angle de contact de la ligne libre et de la paroi du container et la courbure de celle-ci.

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The author studies the two-dimensional problem of the oscillations of a liquid in a symmetrical container under zero gravity. He gives the functional equation of motion and proves the existence of the eigenfrequencies of the liquid under suitable conditions between the contact angle of the free line and of the wall of the container and the curvature of this.

     

Construction,sur un anneau de Dedekind,d'une base reguliere de polynomes a valeurs entieres

Let A be a domain of field of fractions K, and A[X]_sub the ring of integral valued polynomials over A, i. e., polynomials P(X), with coefficients in K, such that P(A) is contained in A. In [2] and [3], P.-J. Cahen characterized the Dedekind domains A for which the A-module A[X]_sub admits a regular basis, i. e. a basis Q₀(X), Q₁(X), ..., Q_n(X), ... such that degQ_n(X)=n for any n.For these Dedekind domains, we give, in this paper, a method to construct explicitly such a basis.     

Forme harmonique duale à un cycle quasi-fuchsienDual harmonic form to a quasi-Fuchsian cycle

Following the ideas of [2,3], we describe an explicit construction of the dual harmonic form to a quasi-Fuchsian surface in a hyperbolic 3-manifold. To cite this article: N. Bergeron, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 395–400.     

Analyse d'un problème de tsunamiAnalysis of a tsunami problem

This article presents a model and a mathematical analysis of a tsunami problem due to the displacement of the lithosphere. We give some results showing the existence, smoothness and uniqueness of the solution. To cite this article: B. Di Martino et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 551–556.     

Sur un problème de type elliptique parabolique non linéaireOn a nonlinear elliptic-parabolic problem

We study the general equation b(u)_t=a(u,?(u)_x)_x+f of elliptic-parabolic type. Using the theory of evolution equation governed by accretive operator, we establish existence and uniqueness of mild solutions to the associate Cauchy problem, under general assumptions on the data. With additional structural condition of Alt–Luckhauss type, we show that the mild solutions are weak solutions. To cite this article: S. Ouaro, H. Touré, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 27–30     

Variétés complexes dont l'éclatée en un point est de FanoComplex manifolds whose blow-up at a point is Fano

We classify complex projective manifolds X for which there exists a point a such that the blow-up of X at a is Fano. As a consequence, we get that, in dimension greater or equal than three, the quadric is the only complex manifold X for which there exists two distinct points a and b such that the blow-up of X with center {a,b} is Fano. To cite this article: L. Bonavero et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 463–468.     

Asymptotic behavior of a stochastic growth process associated with a system of interacting branching random walksComportement asymptotique d'un processus stochastique de croissance associé à un système de marches aléatoires en interaction

We study a continuous time growth process on $\text{Z}{}^{\mathrm{d}}$ (d?1) associated to the following interacting particle system: initially there is only one simple symmetric continuous time random walk of total jump rate one located at the origin; then, whenever a random walk visits a site still unvisited by any other random walk, it creates a new independent random walk starting from that site. Let us call P_d the law of such a process and S⁰_d(t) the set of sites, visited by all walks by time t. We prove that there exists a bounded, non-empty, convex set $\text{C}{}_{\mathrm{d}}\text{?}\text{R}{}^{\mathrm{d}}$, such that for every ε>0, P_d-a.s. eventually in t, the set S_d⁰(t) is within an ε neighborhood of the set [C_dt], where for $\text{A?}\text{R}{}^{\mathrm{d}}$ we define $\text{[A]:=A∩}\text{Z}{}^{\mathrm{d}}$. Moreover, for d large enough, the set C_d is not a ball under the Euclidean norm. We also show that the empirical density of particles within S_d⁰(t) converges weakly to a product Poisson measure of parameter one. To cite this article: A.F. Ram??rez, V. Sidoravicius, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 821–826.     

Sur un théorème de Cauchy–Kowalewski–Nagumo globalOn a global Cauchy–Kowalewski–Nagumo theorem

In this Note, we solve some global linear Cauchy problems. In the holomorphic case, for some operators, our result extends those of [4] when the initial data is in Gevrey class. In the continuous case, we give a generalisation of the local result of N. Nagumo, and on other hand, our result is an extension of the results of [5,1] for Gevrey initial data without the hyperbolicity condition. To cite this article: D. Gourdin, M. Mechab, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 563–567.     

Estimations intérieures avec régularité optimale pour un modèle de plaques en élasticité linéaireInterior estimates with optimal regularity for a plate model in linear elasticity

We are interested in the 3d–2d passage for an asymptotically thin plate in linear elasticity. The classical approach by asymptotic expansion gives an error estimate on the displacements in H¹, assuming the volumic forces at least of regularity L² (and more for certain components). In our work we apply the regularity theory for solutions of elliptic equations. This approach gives, for a new model of Kirchhoff–Love of higher order, an error estimate in H² assuming volumic forces only in L², which is optimal. We also get some interior error estimates in W^k,p, C^k,α. To cite this article: R. Monneau, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 207–212.     

Hypersurfaces compactes d'un fibré vectoriel riemannien à courbure moyenne prescriteCompact hypersurfaces of a Riemannian vector bundle with prescribed mean curvature

Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and Σ the sphere subbundle of E. We look for embeddings of Σ into E admitting prescribed mean curvatures of various types. To cite this article: P. Cherrier, A. Hanani, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 525–528.