http://hdl.handle.net/2268/153 Chercher dans ce canal chercher http://orbi.ulg.ac.be/simple-search http://hdl.handle.net/2268/150773 Titre: Prevalence of nowhere analytic functions <br/> <br/>Auteur, co-auteur: Esser, Céline http://hdl.handle.net/2268/150384 Titre: Au delà des nombres réels <br/> <br/>Auteur, co-auteur: Kreusch, Marie http://hdl.handle.net/2268/150094 Titre: Computing Bounds on the Geometrical Quality of 2D Curvilinear Finite Elements <br/> <br/>Auteur, co-auteur: Johnen, Amaury; Remacle, J.-F.; Toulorge, T.; Lambrechts, J.; Geuzaine, Christophe <br/> <br/>Résumé: The development of high-order computational methods for solving partial differen- tial equations on unstructured grids has been underway for many years. Such meth- ods critically depend on the availability of high-quality curvilinear meshes, as one badly-shaped element can degrade the solution in the whole domain (J. Shewchuk, “What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures”, Preprint, 2002). The usual way of generating curved meshes is to first generate a straight sided mesh and to curve mesh entities that are classified on the boundaries of the domain. The latter operation introduces a “shape-distortion” that should be controlled if we suppose that the straight sided mesh is composed of well-shaped elements. Quality measures allow to quantify to which point an element is well-shaped. They also provide tools to improve the quality of meshes through optimization opera- tions. Many quality measures has been proposed for quadratic triangular finite element. Recently, X. Roca et al. (“Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation”, Proceedings of the 20th Interna- tional Meshing Roundtable, 2011) proposed a technique that allows extending any Jacobian based quality measure for linear elements to high-order iso-parametric planar triangles of any interpolation degree. In this work we propose an efficient method to provide accurate bounds on the mag- nitude of the shape distortion of any triangular and quadrangular curved element. The shape distortion is measured with respect to an ideal element, which can e.g. be an equilateral triangle or the element from the original straight-sided mesh. The key feature of the method is that we can adaptively expand functions based on the Jacobian matrix and its determinant in terms of Be ́zier functions. Be ́zier functions have both properties of boundedness and positivity, which allow sharp computation of minimum or maximum of the interpolated functions. http://hdl.handle.net/2268/150069 Titre: An adaptation of $S^{\nu}$ spaces <br/> <br/>Auteur, co-auteur: Simons, Laurent; Bastin, Françoise; Nicolay, Samuel <br/> <br/>Résumé: The $S^\nu$ spaces have been introduced in 2004 by S. Jaffard in the context of multifractal analysis. In comparison with Besov spaces (the classical functional setting to study signals), these spaces of functions related to the distribution of wavelet coefficients allow to obtain more information on the Hölder regularity of a signal. From a point of view of functional analysis, the $S^nu$ spaces can be considered as sequence spaces (because they are robust). Some properties (topology, complete metric, $p$-locally convexity,...) have been studied. The purpose of the talk is to present the beginning of an adaptation of the $S^nu$ spaces when the discrete wavelet coefficients are replaced by continuous wavelet transform coefficients. http://hdl.handle.net/2268/150068 Titre: Régularité de la fonction de Cantor <br/> <br/>Auteur, co-auteur: Simons, Laurent; Nicolay, Samuel <br/> <br/>Résumé: La fonction de Cantor, bijection entre $[0,1]$ et $[0,1]^2$, est définie via les fractions continues. Par conséquent, il est assez difficile d'avoir une quelconque intuition sur son comportement. Le but de cet exposé est de présenter cette fonction particulière ainsi que sa régularité (continuité et régularité höldérienne). http://hdl.handle.net/2268/150027 Titre: Statistical analysis of incomplete longitudinal ordinal data - Impact of Multiple Imputation on data distribution <br/> <br/>Auteur, co-auteur: Donneau, Anne-Françoise http://hdl.handle.net/2268/150020 Titre: Is there a good way to impute missing data in longitudinal studies with ordinal outcomes ? <br/> <br/>Auteur, co-auteur: Donneau, Anne-Françoise http://hdl.handle.net/2268/149780 Titre: The L-curve for optimal smoothing <br/> <br/>Auteur, co-auteur: Frasso, Gianluca <br/> <br/>Résumé: The L-curve, adopted for the selection of the regularization parameter in ill-posed inverse problems, shows a parametric plot of the residuals vs the penalty. The corner of the L indicates the right amount of regularization. The L-curve is easy to compute and works surprisingly well also for smoothing data with correlated noise. We present the theoretical background, an alternative criterion to nd the corner automatically, and applications to real data. http://hdl.handle.net/2268/149684 Titre: Higher symmetries of the conformal Laplacian <br/> <br/>Auteur, co-auteur: Radoux, Fabian http://hdl.handle.net/2268/149674 Titre: Effets de la qualité des données sur la courbe d'apprentissage des forêts aléatoires <br/> <br/>Auteur, co-auteur: Brostaux, Yves http://hdl.handle.net/2268/149672 Titre: Le problème de Prouhet <br/> <br/>Auteur, co-auteur: Rigo, Michel <br/> <br/>Résumé: Si on pense aux nombres, à leur théorie et à l'arithmétique, on fait rapidement face à de nombreuses questions simples à énoncer (elles ne font intervenir que des sommes, des produits ou des puissances de nombres entiers) mais leurs éventuelles solutions peuvent s'avérer redoutables. Dans ce texte relatif à mon intervention du 22 août 2012 au congrès annuel de la SBPMef, on s'intéressera à un problème accessible : partitionner l'ensemble {0,1,2,...,2^{n+1}-1} en deux sous-ensembles A et B de même taille de telle sorte que les sommes des éléments de A et B soient égales, les sommes des carrés des éléments de A et B soient égales, ..., les sommes des puissances n-ièmes des éléments de A et B soient égales. Par exemple, pour n=2, on trouve 0+3+5+6=1+2+4+7 et 0^2+3^2+5^2+6^2=1^2+2^2+4^2+7^2. On en présentera une solution reposant de façon élégante sur les écritures en base $2$ et on s'autorisera quelques digressions : produit de sinus, répétition et chevauchement, jeu d'échecs, composition musicale, ... Ce texte est construit pour être une balade arithmétique amusante et inattendue, pouvant montrer à des élèves ouverts, un peu comme le prétend André Deledicq, que les mathématiques peuvent être jubilatoires. http://hdl.handle.net/2268/149313 Titre: Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words <br/> <br/>Auteur, co-auteur: Rigo, Michel; Salimov, Pavel <br/> <br/>Résumé: The binomial coefficient of two words u and v is the number of times v occurs as a subsequence of u. Based on this classical notion, we introduce the m-binomial equivalence of two words refining the abelian equivalence. The m-binomial complexity of an infinite word x maps an integer n to the number of m-binomial equivalence classes of factors of length n occurring in x. We study the first properties of m-binomial equivalence. We compute the m-binomial complexity of the Sturmian words and of the Thue-Morse word. We also mention the possible avoidance of 2-binomial squares. <br/> <br/>Commentaires: This is the long version corresponding to the submission (limited to 12 pages). It contains an appendix with the omitted proofs. http://hdl.handle.net/2268/148748 Titre: Prix Nobel d'Economie et mathématiques <br/> <br/>Auteur, co-auteur: Bair, Jacques; Haesbroeck, Gentiane <br/> <br/>Résumé: Le Prix Nobel d'Economie 2012 a été décerné aux deux mathématiciens américains Lloyd Shapley et Alvin Roth. Cet événement nous a donné l'occasion de nous pencher quelque peu sur des prix internationaux pouvant être attribués à des mathématiciens. http://hdl.handle.net/2268/148629 Titre: The number of structures compatible with any given correlation function <br/> <br/>Auteur, co-auteur: Gommes, Cédric http://hdl.handle.net/2268/148592 Titre: Self-shuffling words <br/> <br/>Auteur, co-auteur: Charlier, Emilie http://hdl.handle.net/2268/148591 Titre: Self-shuffling words <br/> <br/>Auteur, co-auteur: Charlier, Emilie; Kamae, Teturo; Puzynina, Svetlana; Zamboni, Luca <br/> <br/>Résumé: In this paper we introduce and study a new property of infinite words which is invariant under the action of a morphism: We say an infinite word x, defined over a finite alphabet A, is self-shuffling if x admits factorizations: x=\prod_{i=1}^\infty U_iV_i=\prod_{i=1}^\infty U_i=\prod_{i=1}^\infty V_i with U_i,V_i \in \A^+. In other words, there exists a shuffle of x with itself which reproduces x. The morphic image of any self-shuffling word is again self-shuffling. We prove that many important and well studied words are self-shuffling: This includes the Thue-Morse word and all Sturmian words (except those of the form aC where a is a letter and C is a characteristic Sturmian word). We further establish a number of necessary conditions for a word to be self-shuffling, and show that certain other important words (including the paper-folding word and infinite Lyndon words) are not self-shuffling. In addition to its morphic invariance, which can be used to show that one word is not the morphic image of another, this new notion has other unexpected applications: For instance, as a consequence of our characterization of self-shuffling Sturmian words, we recover a number theoretic result, originally due to Yasutomi, which characterizes pure morphic Sturmian words in the orbit of the characteristic. http://hdl.handle.net/2268/148516 Titre: Extensions of superalgebras of Krichever-Novikov type <br/> <br/>Auteur, co-auteur: Kreusch, Marie http://hdl.handle.net/2268/148090 Titre: Extensions of Superalgebras of Krichever-Novikov type <br/> <br/>Auteur, co-auteur: Kreusch, Marie http://hdl.handle.net/2268/147977 Titre: Approximation Algorithms for Multi-Dimensional Vector Assignment Problems <br/> <br/>Auteur, co-auteur: Dokka, Trivikram; Crama, Yves; Spieksma, Frits C.R. <br/> <br/>Résumé: We consider a special class of axial multi-dimensional assignment problems called multi-dimensional vector assignment (MVA) problems. An instance of the MVA problem is defined by $m$ disjoint sets, each of which contains the same number $n$ of $p$-dimensional vectors with nonnegative integral components, and a cost function defined on vectors. The cost of an $m$-tuple of vectors is defined as the cost of their component-wise maximum. The problem is now to partition the $m$ sets of vectors into $n$ $m$-tuples so that no two vectors from the same set are in the same $m$-tuple and so that the total cost of the $m$-tuples is minimized. The main motivation comes from a yield optimization problem in semi-conductor manufacturing. We consider two classes of polynomial-time heuristics for MVA, namely, hub heuristics and sequential heuristics, and we study their approximation ratio. In particular, we show that when the cost function is monotone and subadditive, hub heuristics, as well as sequential heuristics, have finite approximation ratio for every fixed $m$. Moreover, we establish better approximation ratios for certain variants of hub heuristics and sequential heuristics when the cost function is monotone and submodular, or when it is additive. We provide examples to illustrate the tightness of our analysis. Furthermore, we show that the MVA problem is APX-hard even for the case $m=3$ and for binary input vectors. Finally, we show that the problem can be solved in polynomial time in the special case of binary vectors with fixed dimension $p$. http://hdl.handle.net/2268/147900 Titre: La fonction exponentielle : premières propriétés <br/> <br/>Auteur, co-auteur: Bair, Jacques; Henry, Valérie <br/> <br/>Résumé: Nous passons en revue différentes façons d'introduire des fonctions exponentielles et logarithmes, montrant notamment comment procédait Euler en exploitant des infinitésimaux.