Factorization of Lipschitz Functioins and Absolute Convergence of Vilenkin-Fourier Series.
Factorizations of matrices and functions of two variables
Failure of the condition N below .
Fermat’s method of quadrature
The Treatise on Quadratureof Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, , or under a higher hyperbola, —with the appropriate limits of integration in each case—has a second part which was mostly unnoticed by Fermat’s contemporaries. This second part of theTreatise is obscure and difficult to read. In it Fermat reduced the quadrature of a great number of algebraic curves in implicit form to the quadrature of known curves: the...
Fields of sets, set functions, set function integrals, and finite additivity.
Filippov's operation and some attributes
Finding new families of rank-one convex polynomials
Finite element approximations of a glaciology problem
In this paper we study a model problem describing the movement of a glacier under Glen’s flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...
Finite element approximations of a glaciology problem
In this paper we study a model problem describing the movement of a glacier under Glen's flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...
First Order Characterizations of Pseudoconvex Functions
First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.
First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints
2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally...
Fonctions convexes et logarithmes de polynômes à coefficients positifs
Fonctions séparément analytiques
On étudie les fonctions de deux variables réelles qui sont séparément analytiques sur un ouvert du plan. On montre que ces fonctions sont analytiques en tout point du domaine de définition hors d’un fermé de ce domaine dont les projections sur chacun des deux axes de coordonnées sont des ensembles polaires. Inversempent, pour tout tel fermé , on construit une fonction séparément analytique dont le domaine d’analyticité est le complémentaire de .
Formules de changement de variables
Formules d'homotopie locales pour le système de Cauchy-Riemann tangentiel
Fractional Iteration and a Generalised Abel's Equation in Two Variables
From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality
We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.
Functional inequality characterizing nonnegative concave functions in (0, ?)k.
Functional inequality characterizing nonnegative concave functions in (0, ?)k. (Summary).
Functions of Bounded mean Oscillation and Quasiconformal Mappings