Ahmed Addou, E. Bekkaye Mermri, Jamal Zahi (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
The aim of this article is to give a regularization method for an unilateral obstacle problem with obstacle and second member , which generalizes the one established by the authors of [4] in case of null obstacle and a second member is equal to constant .
F. Mignosi, A. Restivo, M. Sciortino (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word from a given set of substrings () of a word . We introduce an hypothesis involving the set of fragments and the maximal length of the minimal forbidden factors of . Such hypothesis allows us to reconstruct uniquely the word from the set in linear time....
Flavia Giannetti, Antonia Passarelli di Napoli (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We study the regularity of finite energy solutions to degenerate
Marcus Wagner (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands (, , ) in presence of a convex control restriction. The relaxed problem, wherein the integrand has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image...
Arturo Carpi, Aldo de Luca (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words ...
Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Similarity:
Let = { ∈ | () } be the language recognized by a formal series : → ℝ with isolated cut point . We provide new conditions that guarantee the regularity of the language in the case that is rational or is a Hadamard quotient of rational series. Moreover the decidability property of such conditions is investigated.
Francesco Ghiraldin (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy () −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....
Serge Burckel, Marianne Morillon (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
We construct, for each integer , three functions from {0,1} to {0,1} such that any boolean mapping from {0,1} to {0,1} can be computed with a finite sequence of assignations only using the input variables and those three functions.
Martin Kružík (2013)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝ by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, 86 (1984) 251–277]. As a consequence we get new results on weak...
Arturo Carpi, Aldo de Luca (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
The characteristic parameters and of a word over a finite alphabet are defined as follows: is the minimal natural number such that has no repeated suffix of length and is the minimal natural number such that has no right special factor of length . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution...
Alessio Figalli, Nicola Gigli (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We prove that any Kantorovich potential for the cost function = /2 on a Riemannian manifold (, ) is locally semiconvex in the “region of interest”, without any compactness assumption on , nor any assumption on its curvature. Such a region of interest is of full -measure as soon as the starting measure does not charge – 1-dimensional rectifiable sets.
Romuald Elie, Idris Kharroubi (2014)
ESAIM: Probability and Statistics
Similarity:
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [S. Peng and M. Xu, (2007)] and BSDEs with...
Mette Iversen, Dario Mazzoleni (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We consider the variational problem inf{ () + () + (1 − − ) () | Ω open in ℝ, || ≤ 1}, for ∈ [0, 1], + ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.
Ivan Corwin, Patrik L. Ferrari, Sandrine Péché (2012)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar–Parisi–Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent = 3/2, that means one should find a universal space–time limiting process under the scaling of time as , space like 2/3 and fluctuations like 1/3 as → ∞. In this paper...
Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)
RAIRO - Theoretical Informatics and Applications
Similarity:
Let = { ∈ | () } be the language recognized by a formal series : → ℝ with isolated cut point . We provide new conditions that guarantee the regularity of the language in the case that is rational or is a Hadamard quotient of rational series. Moreover the decidability property of such conditions is investigated.
Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)
RAIRO - Theoretical Informatics and Applications
Similarity:
Let = { ∈ | () } be the language recognized by a formal series : → ℝ with isolated cut point . We provide new conditions that guarantee the regularity of the language in the case that is rational or is a Hadamard quotient of rational series. Moreover the decidability property of such conditions is investigated.
Houman Owhadi, Lei Zhang, Leonid Berlyand (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ( ) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution ) minimizing...
Pedro Ricardo Simão Antunes, Pedro Freitas, James Bernard Kennedy (2013)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We consider the problem of minimising the th-eigenvalue of the Robin Laplacian in R. Although for = 1,2 and a positive boundary parameter it is known that the minimisers do not depend on , we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on . We derive a Wolf–Keller type result for this problem and show that optimal eigenvalues grow at most with , which is in sharp contrast with the Weyl asymptotics for a...
Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...