Displaying similar documents to “Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models”

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Eric Cancès, Rachida Chakir, Yvon Maday (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article, we provide error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to...

Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM

Gabriel N. Gatica, Matthias Maischak, Ernst P. Stephan (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in ℝ n ( ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ω:= ℝ n ∖ Ω ¯ . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping...

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

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Let (Ω, ℱ , ( ℱ t ), ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (the-algebra generated by ( ℱ t )) a coherent family of probability measures ( ℚ t ) indexed by , each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative...

On the optimality of the empirical risk minimization procedure for the convex aggregation problem

Guillaume Lecué, Shahar Mendelson (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We study the performance of (ERM), with respect to the quadratic risk, in the context of , in which one wants to construct a procedure whose risk is as close as possible to the best function in the convex hull of an arbitrary finite class F . We show that ERM performed in the convex hull of F is an optimal aggregation procedure for the convex aggregation problem. We also show that if this procedure is used for the problem of model selection aggregation, in which one wants to mimic the...

Multi-Harnack smoothings of real plane branches

Pedro Daniel González Pérez, Jean-Jacques Risler (2010)

Annales scientifiques de l'École Normale Supérieure

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Let Δ ⊂ 𝐑 2 be an integral convex polygon. G. Mikhalkin introduced the notion of, a class of real algebraic curves, defined by polynomials supported on Δ and contained in the corresponding toric surface. He proved their existence, viamethod, and that the topological type of their real parts is unique (and determined by Δ ). This paper is concerned with the description of the analogous statement in the case of a smoothing of a real plane branch ( C , 0 ) . We introduce the class ofsmoothings of ( C , 0 ) by...

Constructive quantization: approximation by empirical measures

Steffen Dereich, Michael Scheutzow, Reik Schottstedt (2013)

Annales de l'I.H.P. Probabilités et statistiques

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In this article, we study the approximation of a probability measure μ on ℝ d by its empirical measure μ ^ N interpreted as a random quantization. As error criterion we consider an averaged p th moment Wasserstein metric. In the case where 2 p l t ; d , we establish fine upper and lower bounds for the error, a. Moreover, we provide a universal estimate based on moments, a . In particular, we show that quantization by empirical measures is of optimal order under weak assumptions.

Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

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Let 𝔽 F be a filtration andbe a random time. Let 𝔾 G be the progressive enlargement of 𝔽 F with. We study the following formula, called the optional splitting formula: For any 𝔾 G-optional process, there exists an 𝔽 F-optional process and a function defined on [0∞] × (ℝ × ) being ℬ [ 0 , ∞ ] ⊗ 𝒪 ( 𝔽 ) ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y = Y ' 1 [ 0 , τ ) + Y ' ' ( τ ) 1 [ τ , ∞ ) . Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, a W - 1 , N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ℝ N , or on a regular bounded open set of  ℝ N . The proof is based partially on the Strauss inequality [Strauss, 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [ 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and...