Nouvelles propriétés des courbes  et relation 
de dispersion en élasticité linéaire

Tark Bouhennache; Yves Dermenjian

Displaying similar documents to “Nouvelles propriétés des courbes et relation de dispersion en élasticité linéaire”

Complexité et automates cellulaires linéaires

Valérie Berthé (2010)

RAIRO - Theoretical Informatics and Applications

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The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in $ℤ / l ℤ$ , and polynomial initial condition. We prove that the complexity function is quadratic when is a prime and that it increases with respect to the number of distinct prime factors of .

Une note à propos du jacobien de n fonctions holomorphes à l'origine de ℂⁿ

M. Hickel (2008)

Annales Polonici Mathematici

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Let f₁,...,fₙ be n germs of holomorphic functions at the origin of ℂⁿ, such that $f_{i} (0) = 0$ , 1 ≤ i ≤ n. We give a proof based on J. Lipman’s theory of residues via Hochschild homology that the jacobian of f₁,...,fₙ belongs to the ideal generated by f₁,...,fₙ if and only if the dimension of the germ of common zeros of f₁,...,fₙ is strictly positive. In fact, we prove much more general results which are relative versions of this result replacing the field ℂ by convenient noetherian rings A (Ths....

Généralisation d'un théorème de Haagerup

Ferdaous Kellil, Guy Rousseau (2005)

Studia Mathematica

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Let G be a group of automorphisms of a tree X (with set of vertices S) and H a kernel on S × S invariant under the action of G. We want to give an estimate of the $l^{r}$ -operator norm (1 ≤ r ≤ 2) of the operator associated to H in terms of a norm for H. This was obtained by U. Haagerup when G is the free group acting simply transitively on a homogeneous tree. Our result is valid when X is a locally finite tree and one of the orbits of G is the set of vertices at even distance from a given...

Les types de données syntaxiques du système $ℱ$

Samir Farkh, Karim Nour (2010)

RAIRO - Theoretical Informatics and Applications

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We give in this paper a purely syntactical definition of input and output types of system $ℱ$ . We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the -elimination rule in order to prove that an output type is an input type.

Équations elliptiques non linéaires monotones avec un deuxième membre $L^{1}$ ou mesure

François Murat (1998)

Journées équations aux dérivées partielles

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On considère le problème : $\{\begin{matrix} - div a (x, D u) = f dans Ω, \\ u = 0 sur \partial Ω, \end{matrix}$ où $Ω$ est un ouvert borné de $𝐑^{N}$ , où $a (x, ξ)$ est une fonction de Carathéodory, monotone en $ξ$ , coercive, qui définit un opérateur dans $W_{0}^{1, p} (Ω)$ (avec $1 < p \leq N$ ), et où $f$ appartient à $L^{1} (Ω)$ ou est une mesure bornée sur $Ω$ . On introduit une nouvelle définition de la solution de ce problème, la notion de solution renormalisée (ou entropique), et on montre l’existence d’une telle solution et sa continuité par rapport à $f$ . Quand $f$ appartient à $L^{1} (Ω)$ , on montre en outre...

Quantification pour les paires symétriques et diagrammes de Kontsevich

Alberto S. Cattaneo, Charles Torossian (2008)

Annales scientifiques de l'École Normale Supérieure

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In this article we use the expansion for biquantization described in [7] for the case of symmetric spaces. We introduce a function of two variables $E (X, Y)$ for any symmetric pairs. This function has an expansion in terms of Kontsevich’s diagrams. We recover most of the known results though in a more systematic way by using some elementary properties of this $E$ function. We prove that Cattaneo and Felder’s star product coincides with Rouvière’s for any symmetric pairs. We generalize some of...

La structure des sous-espaces de treillis

José L. Marcolino Nhani

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We study some geometrical properties of a new structure introduced by G. Pisier: the structure of lattice subspaces. We show first that if X and Y are Banach lattices such that $B_{r} (X, Y) = B (X, Y)$ , then X is an AL-space or Y is an AM-space. We introduce the notion of homogeneous lattice subspace and we show that up to regular isomorphism, the only homogeneous lattice subspace of $L^{p} (Ω, μ)$ , for 2≤ p < ∞, is G(I). We also show a version of the Dvoretzky theorem for this structure. We end this paper by giving...

Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet

Bernard Bonnard, Monique Chyba (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Consider a where is a neighborhood of 0 in , is a identified to ker , being the 1-form: $ω = d z - \frac{y^{2}}{2} d x$ , and is a on which can be taken in the : $g = a (q) d x^{2} + c (q) d y^{2}$ , , , $G_{|_{x = y = 0}} = 0$ . In a previous article we analyze : ; we describe the , the and the . The objectif of this article is to provide a geometric and computational framework to analyze the general case. This frame is obtained by analysing three of the flat case which clarify the role of the three parameters $α, β, γ$ in the where:...

Plus grand facteur premier de valeurs de polynômes aux entiers

R. de la Bretèche (2015)

Acta Arithmetica

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Let P⁺(n) denote the largest prime factor of the integer n. Using the Heath-Brown and Dartyge methods, we prove that for any even unitary irreducible quartic polynomial Φ with integral coefficients and the associated Galois group isomorphic to V₄, there exists a positive constant $c_{Φ}$ such that the set of integers n ≤ X satisfying $P ⁺ (Φ (n)) \geq X^{1 + c_{Φ}}$ has a positive density. Such a result was recently proved by Dartyge for Φ(n) = n⁴ - n² + 1. There is an appendix written with Jean-François Mestre. ...

Courbes elliptiques sur ℚ, ayant un point d’ordre 2 rationnel sur ℚ, de conducteur $2^{N} p$

Wilfrid Ivorra

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Let p be a prime number ≥ 29 and N be a positive integer. In this paper, we are interested in the problem of the determination, up to ℚ-isomorphism, of all the elliptic curves over ℚ whose conductor is $2^{N} p$ , with at least one rational point of order 2 over ℚ. This problem was studied in 1974 by B. Setzer in case N = 0. Consequently, in this work we are concerned with the case N ≥ 1. The results presented here are analogous to those obtained by B. Setzer and allow one in practice to find...

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Théorèmes de préparation Gevrey et étude de certaines applications formelles

Augustin Mouze (2003)

Annales Polonici Mathematici

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We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from $ℂ^{s}$ to $ℂ^{p}$ without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent...

Espaces de suites réelles complètement métrisables

Pierre Casevitz (2001)

Fundamenta Mathematicae

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Let X be an hereditary subspace of the Polish space $ℝ^{ω}$ of real sequences, i.e. a subspace such that [x = (xₙ)ₙ ∈ X and ∀n, |yₙ| ≤ |xₙ|] ⇒ y = (yₙ)ₙ ∈ X. Does X admit a complete metric compatible with its vector structure? We have two results: ∙ If such an X has a complete metric δ, there exists a unique pair (E,F) of hereditary subspaces with E ⊆ X ⊆ F, (E,δ) complete separable, and F complete maximal in a strong sense. On E and F, the metrics have a simple form, and the spaces E are...

Propagation de la 2-birationalité

Claire Bourbon, Jean-François Jaulent (2013)

Acta Arithmetica

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Let L/K be a 2-birational CM-extension of a totally real 2-rational number field. We characterize in terms of tame ramification totally real 2-extensions K’/K such that the compositum L’=LK’ is still 2-birational. In case the 2-extension K’/K is linearly disjoint from the cyclotomic ℤ₂-extension $K^{c} / K$ , we prove that K’/K is at most quadratic. Furthermore, we construct infinite towers of such 2-extensions.