Propagation de la 2-birationalité

Claire Bourbon; Jean-François Jaulent

Displaying similar documents to “Propagation de la 2-birationalité”

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....

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...

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...

Contre-exemples au principe de Hasse pour les courbes de Fermat

Alain Kraus (2016)

Acta Arithmetica

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Let p be an odd prime number. In this paper, we are concerned with the behaviour of Fermat curves defined over ℚ, given by equations $a x^{p} + b y^{p} + c z^{p} = 0$ , with respect to the local-global Hasse principle. It is conjectured that there exist infinitely many Fermat curves of exponent p which are counterexamples to the Hasse principle. This is a consequence of the abc-conjecture if p ≥ 5. Using a cyclotomic approach due to H. Cohen and Chebotarev’s density theorem, we obtain a partial result towards this conjecture,...

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 .

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. ...

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...

Extensions de jets dans des intersections de classes non quasi-analytiques

P. Beaugendre (2001)

Annales Polonici Mathematici

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In [3], J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset E of ℝⁿ, in the case of intersections of non-quasi-analytic classes with moderate growth and a Łojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every $C^{\infty}$ -Whitney jet belongs to one of them. We also prove a linear...

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...

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...

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.

Théorème de la clôture lq-modulaire et applications

Mustapha Chellali, El hassane Fliouet (2011)

Colloquium Mathematicae

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Let K be a purely inseparable extension of a field k of characteristic p ≠ 0. Suppose that $[k : k^{p}]$ is finite. We recall that K/k is lq-modular if K is modular over a finite extension of k. Moreover, there exists a smallest extension m/k (resp. M/K) such that K/m (resp. M/k) is lq-modular. Our main result states the existence of a greatest lq-modular and relatively perfect subextension of K/k. Other results can be summarized in the following: 1. The product of lq-modular extensions over k is...

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...

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....

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...

Sur une application de la formule de Selberg-Delange

F. Ben Saïd, J.-L. Nicolas (2003)

Colloquium Mathematicae

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E. Landau has given an asymptotic estimate for the number of integers up to x whose prime factors all belong to some arithmetic progressions. In this paper, by using the Selberg-Delange formula, we evaluate the number of elements of somewhat more complicated sets. For instance, if ω(m) (resp. Ω(m)) denotes the number of prime factors of m without multiplicity (resp. with multiplicity), we give an asymptotic estimate as x → ∞ of the number of integers m satisfying $2^{ω (m)} m \leq x$ , all prime factors...

Derivees tangentielles des fonctions de la classe $^{k, α}$ dans les domaines de type fini de ℂ²

Laurent Verdoucq (2002)

Annales Polonici Mathematici

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Let Ω be a domain of finite type in ℂ² and let f be a function holomorphic in Ω and belonging to $^{k, α} (Ω ̅)$ . We prove the existence of boundary values for some suitable derivatives of f of order greater than k. The gain of derivatives holds in the complex-tangential direction and it is precisely related to the geometry of ∂Ω. Then we prove a property of non-isotropic Hölder regularity for these boundary values. This generalizes some results given by J. Bruna and J. M. Ortega for the unit ball. ...

$L^{p} (G, X )$ comme sous-espace complémenté de $L^{q} (G, X) $

Mohammad Daher (2013)

Colloquium Mathematicae

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Let G be a compact metric infinite abelian group and let X be a Banach space. We study the following question: if the dual X* of X does not have the Radon-Nikodym property, is $L^{p} (G, X *)$ complemented in $L^{q} (G, X) *$ , 1 < p ≤ ∞, 1/p + 1/q = 1, or, if p = 1, in the subspace of C(G,X)* consisting of the measures that are absolutely continuous with respect to the Haar measure? We show that the answer is negative if X is separable and does not contain ℓ¹, and if 1 ≤ p < ∞. If p = 1, this answers a question...

Nouvelles propriétés des courbes et relation de dispersion en élasticité linéaire

Tark Bouhennache, Yves Dermenjian (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In the case of an elastic strip we exhibit two properties of dispersion curves , that were not pointed out previously. We show cases where and we point out that these curves are not automatically monotoneous on $ℝ_{+}$ . The non monotonicity was an open question (see [2], for example) and, for the first time, we give a rigourous answer. Recall the characteristic property of the dispersion curves: {} is the set of eigenvalues of , counted with their multiplicity. The operators...