University of Marne-la-Vallée

About: University of Marne-la-Vallée is a based out in . It is known for research contribution in the topics: Estimator & Context (language use). The organization has 831 authors who have published 1855 publications receiving 55316 citations.

Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations

Abstract: Introduction Section 1: Preliminaries 1.1 The Navier-Stokes equations 1.2 Classical, mild and weak solutions 1.3 Navier meets Fourier Section 2: Functional setting of the equations 2.1 The Littlewood-Paley decomposition 2.2 The Besov spaces 2.3 The paraproduct rule 2.4 The wavelet decomposition 2.5 Other useful function spaces Section 3: Existence theorems 3.1 The fixed point theorem 3.2 Scaling invariance 3.3 Super-critical case

Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

Abstract: The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing, in particular, several characterizations of such thresholders. We then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and we establish the strong convergence of a proximal thresholding algorithm to solve it. Numerical applications to signal recovery are demonstrated.

Multiple recurrence and nilsequences

Abstract: Aiming at a simultaneous extension of Khintchine’s and Furstenberg’s Recurrence theorems, we address the question if for a measure preserving system $(X,\mathcal{X},\mu,T)$ and a set $A\in\mathcal{X}$ of positive measure, the set of integers n such that $\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon$ is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for k≥4 it is not. The main tool is a decomposition result for the multicorrelation sequence $\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)}$ , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d*(E)>0 and for all e>0, the set $$\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}$$ is syndetic.

Ab initio and experimental pre-edge investigations of the Mn K -edge XANES in oxide-type materials

Abstract: Mn $K$ edge ab initio FEFF8.2 calculations of the pre-edge features of the x-ray-absorption near-edge structure (XANES) region were undertaken for a series of Mn-bearing oxide-type compounds. The aim of the study is to provide a reliable method for determining quantitative and accurate redox and symmetry information for manganese. In agreement with multiplet calculations by Glatzel and co-workers, FEFF8.2 predicts a doublet and a triplet for Mn(II) and Mn(III) in octahedral symmetry, respectively, in agreement with high-resolution XANES experiments. Site distortion increases notably the contribution from dipolar transitions and, consequently, the pre-edge feature integrated area. An even more intense pre-edge feature is calculated and measured for the ${T}_{d}$ symmetry (singletlike). For Mn(IV), a triplet is predicted and measured for the ${O}_{h}$ symmetry. However, additional transitions are found in Mn(IV)-rich compounds, that are related to metal-metal transitions. These transitions overlap strongly with the ``true pre-edge,'' making extraction of redox and symmetry information for Mn(IV) more challenging. However, a model of the pre-edge with pseudo-Voigt functions of fixed calculated width (based on core-hole lifetime and experimental resolution) helps to separate the contributions related to first-neighbor symmetry from those of the metal-metal pairs. Application to multivalent defective manganese oxide materials suggests that the pre-edge information varies linearly as a function of Mn redox state or symmetry but varies nonlinearly as a function of both parameters. Finally, the polymerization of the manganese networks can be estimated from the metal-metal transitions found in the pre-edge region.