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Analyse 2-microlocale et développementen série de chirps d'une fonction de Riemann et de ses généralisations

Daniel Boichu (1994)

Colloquium Mathematicae

En dimension 1 on analyse la fonction irrégulière r ( x ) = ∑ n = 1 ∞ n - p s i n ( n p x ) (p entier ≥ 2) en un point x 0 de dérivabilité (π est un tel point) et on démontre que le terme d’erreur est un chirp de classe (1 + 1/(2p-2), 1/(p-1), (p-1)/p). La fonction r(x) est dans l’espace 2-microlocal C x 0 s , s ' si et seulement si s+s’ ≤ 1 - 1/p et ps+s’≤ p - 1/2. En dimension 2, on obtient en (π,π) l’existence d’un plan tangent pour la surface z = ∑ m , n = 1 ∞ ( m 2 + n 2 ) - γ s i n ( m 2 x + n 2 y ) dès que γ>1.

Analyse de récession et résultats de stabilité d’une convergence variationnelle, application à la théorie de la dualité en programmation mathématique

Driss Mentagui (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Soit X un espace de Banach de dual topologique X ' . 𝒞 X (resp. 𝒞 X ' ) désigne l’ensemble des parties non vides convexes fermées de X (resp. w * -fermées de X ' ) muni de la topologie de la convergence uniforme sur les bornés des fonctions distances. Cette topologie se réduit à celle de la métrique de Hausdorff sur les convexes fermés bornés [16] et admet en général une représentation en terme de cette dernière [11]. De plus, la métrique qui lui est associée s’est révélée très adéquate pour l’étude quantitative...

Analyse de récession et résultats de stabilité d'une convergence variationnelle, application à la théorie de la dualité en programmation mathématique

Driss Mentagui (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let X be a Banach space and X' its continuous dual. C(X) (resp. C(X')) denotes the set of nonempty convex closed subsets of X (resp. ω*-closed subsets of X') endowed with the topology of uniform convergence of distance functions on bounded sets. This topology reduces to the Hausdorff metric topology on the closed and bounded convex sets [16] and in general has a Hausdorff-like presentation [11]. Moreover, this topology is well suited for estimations and constructive approximations [6-9]. We...

Analyse relative

Yves Peraire (1992)

Annales scientifiques de l'Université de Clermont. Mathématiques

Analytic Baire spaces

A. J. Ostaszewski (2012)

Fundamenta Mathematicae

We generalize to the non-separable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a joint-continuity result for non-separable normed groups, previously known only in the separable context.

Analytic functions are ℐ -density continuous

Krzysztof Ciesielski, Lee Larson (1994)

Commentationes Mathematicae Universitatis Carolinae

A real function is ℐ -density continuous if it is continuous with the ℐ -density topology on both the domain and the range. If f is analytic, then f is ℐ -density continuous. There exists a function which is both C ∞ and convex which is not ℐ -density continuous.

Analytical properties of power series on Levi-Civita fields

Khodr Shamseddine, Martin Berz (2005)

Annales mathématiques Blaise Pascal

A detailed study of power series on the Levi-Civita fields is presented. After reviewing two types of convergence on those fields, including convergence criteria for power series, we study some analytical properties of power series. We show that within their domain of convergence, power series are infinitely often differentiable and re-expandable around any point within the radius of convergence from the origin. Then we study a large class of functions that are given locally by power series and...

Anisotropic functions : a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...

Anisotropic functions: a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In the 1950's and 1960's surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...

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