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ORBi Open Repository and Bibliography (319.770 recursos)

In may 2007, the ULg's Administrative Board (joined in June 2007 by the FUSAGx) decided to create an institutional repository and defined a strong institutional self-archiving policy to increase the visibility, accessibility and impact of the University's publications (Board's decision). This decision led to the official launch, in November 2008, of the ORBi platform including both the Academic Bibliography and the Institutional Repository of the Wallonia-Europe University Academy.

Physical, chemical, mathematical & earth Sciences => Mathematics

Mostrando recursos 1 - 20 de 225

  1. Diametral dimensions and some applications to spaces Snu

    Demeulenaere, Loïc
    The "classic" diametral dimension is a topological invariant which characterizes Schwartz and nuclear locally convex spaces. Besides, there exists a second diametral dimension which is conjectured to be equal to the first one (on Fréchet-Schwartz spaces). The first part of this thesis is dedicated to the study of this conjecture. We present several positive partial results in metrizable spaces (in particular in Köthe sequence spaces and Hilbertizable spaces) and some properties which provide the equality of the two diametral dimensions (such as the Delta-stability, the existence of prominent bounded sets, and the property Omega bar). Then, we describe the construction of some non-metrizable locally...

  2. Some generalizations of the Pascal triangle: base 2 and beyond

    Stipulanti, Manon
    The binomial coefficient (u,v) of two finite words u and v (on a finite alphabet) is the number of times the word v appears inside the word u as a subsequence (or, as a "scattered" subword). For instance, (abbabab,ab)=4. This concept naturally extends the classical binomial coefficients of integers, and has been widely studied for about thirty years (see, for instance, Simon and Sakarovitch). In this talk, I present the research lead from October 2015: I give the main ideas that lead to an extension of the Pascal triangles to base-2 expansions of integers. After that, I extend the work...

  3. Pascal-like triangles: base 2 and beyond

    Stipulanti, Manon
    The binomial coefficient (u,v) of two finite words u and v (on a finite alphabet) is the number of times the word v appears inside the word u as a subsequence (or, as a "scattered" subword). For instance, (abbabab,ab)=4. This concept naturally extends the classical binomial coefficients of integers, and has been widely studied for about thirty years (see, for instance, Simon and Sakarovitch). In this talk, I present the research lead since October 2015: I give the main ideas that give an extension of the Pascal triangle to base-2 expansions of integers and also give an overview of the...

  4. From combinatorial games to shape-symmetric morphisms

    Rigo, Michel
    Siegel suggests in his book on combinatorial games that quite simple games provide us with challenging problems: ``No general formula is known for computing arbitrary Grundy values of Wythoff's game. In general, they appear chaotic, though they exhibit a striking fractal-like pattern.''. This observation is the first motivation behind this chapter. We present some of the existing connections between combinatorial game theory and combinatorics on words. In particular, multidimensional infinite words can be seen as tiling of $N^d$. They naturally arise from subtraction games on $d$ heaps of tokens. We review notions such as $k$-automatic, $k$-regular or shape-symmetric multidimensional words....

  5. An optimized domain decomposition method between interior and exterior domains for harmonic, penetrable and inhomogeneous electromagnetic scattering problems

    Caudron, Boris; Geuzaine, Christophe; Antoine, Xavier
    Peer reviewed

  6. A well-conditioned weak coupling between interior and exterior domains for harmonic electromagnetic scattering

    Caudron, Boris; Antoine, Xavier; Geuzaine, Christophe
    Peer reviewed

  7. Combinatoire des mots : résultats classiques et avancées récentes

    Rigo, Michel
    Dans cet exposé ne nécessitant aucun prérequis, je présenterai quelques grands thèmes issus de la combinatoire des mots (i.e., des suites prenant leurs valeurs dans un ensemble fini de symboles) et leurs possibles applications en théorie des nombres, en dynamique symbolique ou en géométrie discrète. En guise d'illustration, considérons le problème suivant. Un carré est la répétition de deux facteurs consécutifs identiques. Ainsi, le mot "entente" débute par le carré (ent)^2 et se aussi termine par le carré (nte)^2. Etant donné un alphabet de taille fixée, on souhaite construire un mot, le plus long possible, évitant un motif particulier. On se...

  8. Sequences, Groups, and Number Theory


    This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is...

  9. INVESTIGATING LUNAR TOPOGRAPHIC PROPERTIES AT DIFFERENT SPATIAL SCALES USING DATA FROM THE LUNAR ORBITER LASER ALTIMETER AND THE WAVELET LEADERS METHOD

    Lemelin, Myriam; Daly, Mike; Deliège, Adrien
    Peer reviewed

  10. Des mathématiques derrière l'intelligence artificielle

    Deliège, Adrien

  11. Les groupes automatiques

    Leroy, Julien

  12. Les systèmes de numération en base rationnelle

    Leroy, Julien

  13. Utilisation d'un microscope mathématique pour étudier des phénomènes irréguliers

    Esser, Céline
    Concours de vulgarisation scientifique "Ma thèse en 180 secondes"

  14. MATh.en.JEANS


    Ce livre recueille 6 articles écrits par 20 élèves ayant participé à l'initiative MeJ.be en 2016-2017, ainsi qu'un descriptif du congrès organisé à Liège au mois d’avril 2017 durant lequel ces mêmes participants sont venus présenter leurs résultats, en compagnie de près de 300 autres jeunes venus de Belgique, de France et du Luxembourg. Dans ces quelques pages vous découvrirez, chers lecteurs, des problèmes simples à poser mais qui ouvrent des portes vers des trésors de réflexion et vous aurez l’occasion de suivre le raisonnement de jeunes adolescents qui les ont abordé avec très peu d’outils à leur disposition. A...

  15. Examples and counter-examples about the S-adic conjecture.

    Leroy, Julien
    Peer reviewed

  16. Return words in tree sets

    Leroy, Julien
    Peer reviewed

  17. Some improvements of the S-adic conjecture (extended abstract)

    Leroy, Julien
    Peer reviewed

  18. Groupe de dimension de système dynamique, partie 1

    Leroy, Julien

  19. Counting Subwords Occurrences in Base-b Expansions

    Leroy, Julien; Rigo, Michel; Stipulanti, Manon
    Peer reviewed

  20. Deux siècles de statistique à l'Université de Liège

    Bair, Jacques
    Pendant deux siècles, l’enseignement et la recherche en statistique et en probabilité ont fortement évolué à l’Université de Liège, en étant fort discrets à la naissance pour devenir imposants au moment du bicentenaire. Le but de ce livre consiste à mettre en évidence cette progression. Pour comprendre le cheminement suivi, l’histoire des deux disciplines concernées a été brièvement retracée. Ensuite, un regard est jeté sur le passé ; on y analyse en détail l’émergence de la statistique dans les diverses Facultés, spécialement dans celles de Sciences, de Droit et de Médecine. De plus, des éléments biographiques sont donnés sur sept statisticiens...

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