Fonctionnelle

Résumé

Une fonctionnelle, en mathématiques, est une application d'un espace vectoriel — généralement un espace vectoriel de fonctions — vers son corps de scalaires. Lorsqu'une fonctionnelle est linéaire, on parle de forme linéaire. Ce terme peut également être utilisé comme adjectif correspondant au nom fonction — voir par exemple programmation fonctionnelle. Référence , , : Voir aussi

Distribution (mathématiques)
Espace dual

Catégorie:Analyse (mathématiques)

Source officielle

https://fr.wikipedia.org/wiki/Fonctionnelle

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vignette|Une photographie de David Hilbert (1862 - 1943) qui a donné son nom aux espaces dont il est question dans cet article. En mathématiques, un espace de Hilbert est un espace vectoriel réel (re

vignette|Diagramme de calcul pour la fonction x \mapsto \frac{2x-1}{x+3} En mathématiques, une fonction permet de définir un résultat (le plus souvent numérique) pour chaque valeur d’un

L'analyse fonctionnelle est la branche des mathématiques et plus particulièrement de l'analyse qui étudie les espaces de fonctions. Elle prend ses racines historiques dans l'étude des transformation

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Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve and is therefore described by a polynomial equation with complex coefficients. The uniformization problem is then to link explicitly these two descriptions. In [BS05b], Peter Buser and Robert Silhol develop a new uniformization method for compact Riemann surfaces of genus two. Given such a surface S, the method describes a polynomial equation of an algebraic curve conformally equivalent to S. However, in this method appear a complex number τ BS and a function f BS which is holomorphic on the unit disk, both being characterized by some functional equations. This means that τ BS, f BS are given implicitly. P. Buser and R. Silhol then approximate them numerically by a complex number τ and a polynomial p using the approximation method developped in [BS05a]. In cases where the equation of the algebraic curve is known, they notice that these approximations are very good. In this thesis we prove a convergence theorem for the approximation method of P. Buser and R. Silhol, and we propose an adaptation of their method that allows to solve some of the numerical problems to which it is prone. Moreover, we generalize this uniformization method to hyperelliptic Riemann surfaces of genus greater than 2, and we give some examples of numerical uniformization in genus 3.

EPFL2010

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AMPK alpha 1-LDH pathway regulates muscle stem cell self-renewal by controlling metabolic homeostasis

Laurent Bultot, Caterina Collodet, Kei Sakamoto, Lin Yang

Control of stem cell fate to either enter terminal differentiation versus returning to quiescence (self-renewal) is crucial for tissue repair. Here, we showed that AMP-activated protein kinase (AMPK), the master metabolic regulator of the cell, controls muscle stem cell (MuSC) self-renewal. AMPK alpha 1(-/-) MuSCs displayed a high self-renewal rate, which impairs muscle regeneration. AMPK alpha 1(-/-) MuSCs showed a Warburg-like switch of their metabolism to higher glycolysis. We identified lactate dehydrogenase (LDH) as a new functional target of AMPK alpha 1. LDH, which is a non-limiting enzyme of glycolysis in differentiated cells, was tightly regulated in stem cells. In functional experiments, LDH overexpression phenocopied AMPK alpha 1(-/-) phenotype, that is shifted MuSC metabolism toward glycolysis triggering their return to quiescence, while inhibition of LDH activity rescued AMPK alpha 1(-/-) MuSC self-renewal. Finally, providing specific nutrients (galactose/glucose) to MuSCs directly controlled their fate through the AMPK alpha 1/LDH pathway, emphasizing the importance of metabolism in stem cell fate.

Wiley2017

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System for planning and/or providing neuromodulation, especially neurostimulation

Miroslav Caban, Marco Capogrosso, Grégoire Courtine, Vincent Delattre, Karen Minassian, Fabien Bertrand Paul Wagner

The present invention relates system for planning and/or providing neuromodulation (10), especially neurostimulation, comprising - a neurostimulator (24) comprising a least one electrode (22), - functional mapping module (38) configured and arranged such that based on stimulation related basic data and stimulation related response data and transfer data a digital characteristic functional map is generated and/or provided, which describes the interrelation between the stimulation related basic data and the stimulation related response data and the transfer data, and - analysis module (42) configured and arranged such that the digital characteristic functional map can be analyzed in connection with neurostimulation provided by the neurostimulator such that the provided neurostimulation and and its response can be analyzed on the basis of the functional map and that on the basis of this analysis an placement analysis of the placement of the electrode is provided.

2019

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