Displaying similar documents to “Les I-types du système

Sur un problème parabolique-elliptique

Philippe Benilan, Petra Wittbold (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like ( v - 1 ) t + = v x x + F ( v ) x where the function F : is only supposed to be locally lipschitz continuous. In order to replace the lack of compactness in on , we use nonlinear semigroup theory.

Sur les courbes hyperelliptiques cyclotomiques et les équations x p - y p = c z ²

Wilfrid Ivorra

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Let p be a prime number ≥ 11 and c be a square-free integer ≥ 3. In this paper, we study the diophantine equation x p - y p = c z ² in the case where p belongs to 11,13,17. More precisely, we prove that for those primes, there is no integer solution (x,y,z) to this equation satisfying gcd(x,y,z) = 1 and xyz ≠ 0 if the integer c has the following property: if ℓ is a prime number dividing c then ℓ ≢ 1 mod p. To obtain this result, we consider the hyperelliptic curves C p : y ² = Φ p ( x ) and D p : p y ² = Φ p ( x ) , where Φ p is the pth cyclotomic...

Une formule pour les extensions de foncteurs composés

Alain Troesch (2003)

Fundamenta Mathematicae

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Let p be a prime, and let ℱ be the category of functors from the finite p -vector spaces to all p -vector spaces. The object Id of ℱ is the inclusion functor. Let F and G be two objects in ℱ. If F and G satisfy suitable conditions, the main result of this paper allows one to compute E x t * ( I d , G F ) from the knowledge of E x t * ( I d , F ) and E x t * ( I d , G ) .

Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz

Rimer Zurita (2013)

Acta Arithmetica

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Let Ω(n) and ω(n) denote the number of distinct prime factors of the positive integer n, counted respectively with and without multiplicity. Let d k ( n ) denote the Piltz function (which counts the number of ways of writing n as a product of k factors). We obtain a precise estimate of the sum n x , Ω ( n ) - ω ( n ) = q f ( n ) for a class of multiplicative functions f, including in particular f ( n ) = d k ( n ) , unconditionally if 1 ≤ k ≤ 3, and under some reasonable assumptions if k ≥ 4. The result also applies to f(n) = φ(n)/n (where φ is...

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Cyril Agrafeuil (2005)

Studia Mathematica

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We denote by the unit circle and by the unit disc of ℂ. Let s be a non-negative real and ω a weight such that ω ( n ) = ( 1 + n ) s (n ≥ 0) and the sequence ( ω ( - n ) / ( 1 + n ) s ) n 0 is non-decreasing. We define the Banach algebra A ω ( ) = f ( ) : | | f | | ω = n = - + | f ̂ ( n ) | ω ( n ) < + . If I is a closed ideal of A ω ( ) , we set h ( I ) = z : f ( z ) = 0 ( f I ) . We describe all closed ideals I of A ω ( ) such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra A s ( ) = f A ω ( ) : f ̂ ( n ) = 0 ( n < 0 ) without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating...

Présentation jordanienne de l'algèbre de Weyl A₂

J. Alev, F. Dumas (2001)

Annales Polonici Mathematici

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Let k be a commutative field. For any a,b∈ k, we denote by J a , b ( k ) the deformation of the 2-dimensional Weyl algebra over k associated with the Jordanian Hecke symmetry with parameters a and b. We prove that: (i) any J a , b ( k ) can be embedded in the usual Weyl algebra A₂(k), and (ii) J a , b ( k ) is isomorphic to A₂(k) if and only if a = b.

Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions

David Mascré (2006)

Colloquium Mathematicae

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On a metric measure space (X,ϱ,μ), consider the weight functions w α ( x ) = ϱ ( x , z ) - α if ϱ(x,z₀) < 1, w α ( x ) = ϱ ( x , z ) - α if ϱ(x,z₀) ≥ 1, w β ( x ) = ϱ ( x , z ) - β if ϱ(x,z₀) < 1, w β ( x ) = ϱ ( x , z ) - β if ϱ(x,z₀) ≥ 1, where z₀ is a given point of X, and let κ a : X × X be an operator kernel satisfying κ a ( x , y ) c ϱ ( x , y ) a - d for all x,y ∈ X such that ϱ(x,y) < 1, κ a ( x , y ) c ϱ ( x , y ) a - D for all x,y ∈ X such that ϱ(x,y)≥ 1, where 0 < a < min(d,D), and d and D are respectively the local and global volume growth rate of the space X. We determine conditions on a, α₀, α₁, β₀, β₁ ∈ ℝ for the Hardy-Littlewood-Sobolev...

Fonctions maximales centrées de Hardy-Littlewood sur les groupes de Heisenberg

Hong-Quan Li (2009)

Studia Mathematica

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By getting uniformly asymptotic estimates for the Poisson kernel on Heisenberg groups 2 n + 1 , we prove that there exists a constant A > 0, independent of n ∈ ℕ*, such that for all f L ¹ ( 2 n + 1 ) , we have | | M f | | L 1 , A n | | f | | , where M denotes the centered Hardy-Littlewood maximal function defined by the Carnot-Carathéodory distance or by the Korányi norm.

Espaces BMO, inégalités de Paley et multiplicateurs idempotents

Hubert Lelièvre (1997)

Studia Mathematica

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Generalizing the classical BMO spaces defined on the unit circle with vector or scalar values, we define the spaces B M O ψ q ( ) and B M O ψ q ( , B ) , where ψ q ( x ) = e x q - 1 for x ≥ 0 and q ∈ [1,∞[, and where B is a Banach space. Note that B M O ψ 1 ( ) = B M O ( ) and B M O ψ 1 ( , B ) = B M O ( , B ) by the John-Nirenberg theorem. Firstly, we study a generalization of the classical Paley inequality and improve the Blasco-Pełczyński theorem in the vector case. Secondly, we compute the idempotent multipliers of B M O ψ q ( ) . Pisier conjectured that the supports of idempotent multipliers of...

Feuilletages holomorphes de codimension un dont la classe canonique est triviale

Frédéric Touzet (2008)

Annales scientifiques de l'École Normale Supérieure

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We give a description of Kähler manifolds M equipped with an integrable subbundle of T M of rank n - 1 ( n = dim M ) under the assumption that the line bundle D é t is numerically trivial. This is a sort of foliated version of Bogomolov’s theorem concerning Kähler manifolds with trivial canonical class.

Les types de données syntaxiques du système

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 . 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.

Stabilité L 1 d’ondes progressives de lois de conservation scalaires

Denis Serre (1998-1999)

Séminaire Équations aux dérivées partielles

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A powerfull method has been developped in [2] for the study of L 1 -stability of travelling waves in conservation laws or more generally in equations which display L 1 -contractivity, maximum principle and mass conservation. We recall shortly the general procedure. We also show that it partly applies to the waves of a model of radiating gas. These waves have first been studied by Kawashima and Nishibata [5,6] in a different framework. Therefore, shock fronts for this model are stable under...

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...

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 - 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:...

Unicité forte à l'infini pour KdV

Luc Robbiano (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Dans ce papier nous prouvons que si une solution de KdV est suffisamment décroissante à l'infini (c'est-à-dire comme e - x α α > 9 / 4 ) et si la donnée de Cauchy est nulle pour assez grand alors la solution est nulle. Ce résultat est la conséquence d'une inégalité de Carleman adaptée à la décroissance de la solution à l'infini.