extensions of functions and stabilization of Glaeser refinements.
weakly chaotic functions with zero topological entropy and non- flat critical points.
-antiderivatives of -adic -functions
-diffeomorphismen semianalytischer und subanalytischer Mengen
-minimal pairs of compact convex sets.
C1,... partial regularity of functions minimising quasiconvex integrals.
Calcul différentiel dans les espaces vectoriels topologiques
Calcul d'Ito sans probabilités
Calcul Moulien
Ce texte est une introduction au calcul moulien, développé par Jean Écalle. On donne une définition précise de la notion de moule ainsi que les principales propriétés de ces objets. On interprète les différentes symétries (alterna(e)l,symetra(e)l) des moules via les séries formelles non commutatives associées dans des bigèbres graduées notées et , correspondant aux deux types de colois étudiées par Ecalle, à savoir et . On illustre en détail l’application de ce formalisme dans le domaine de...
Calculation of improper integrals using uniformly distributed sequences
Calculations of graded ill-known sets
To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the...
Calculus of Variations with Classical and Fractional Derivatives
MSC 2010: 49K05, 26A33We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.
Canonical Banach function spaces generated by Urysohn universal spaces. Measures as Lipschitz maps
It is proved (independently of the result of Holmes [Fund. Math. 140 (1992)]) that the dual space of the uniform closure of the linear span of the maps x ↦ d(x,a) - d(x,b), where d is the metric of the Urysohn space of diameter r, is (isometrically if r = +∞) isomorphic to the space of equivalence classes of all real-valued Lipschitz maps on . The space of all signed (real-valued) Borel measures on is isometrically embedded in the dual space of and it is shown that the image of the embedding...
Canonical decompositions of certain generalized Brownian bridges.
Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue
Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress- strain behavior of soft biological tissues is extended into a viscoelastic material model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a three-dimensional constitutive model that is suitable for general analysis. The model is derived in a configuration that differs from the current, or spatial,...
Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative
2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional derivatives,...
Caractère lipschitzien d'une distance associée à des champs de vecteurs engendrant une algèbre de Lie de rang maximal. Quelques conséquences
La métrique attachée de façon naturelle à des champs de vecteurs est susceptible de plusieurs définitions voisines ; on montre que, suivant la définition adoptée, elle peut avoir, ou ne pas avoir, un caractère localement lipschitzien qui a pour conséquence l’existence de points -réguliers, pour certains opérateurs différentiels , sur les frontières des boules pour la métrique.
Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.
Given a subring of the ring of formal power series defined by the growth of the coefficients, we prove a necessary and sufficient condition for it to be a noetherian ring. As a particular case, we show that the ring of Gevrey power series is a noetherian ring. Then, we get a spectral synthesis theorem for some classes of ultradifferentiable functions.
Caractérisation tangentielle des classes de Carleman de fonctions holomorphes
Carleman's inequality – history, proofs and some new generalizations.