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Titre : A la découverte des graphes et des algorithmes de graphes Type de document : Guide/Manuel Auteurs : Christian Laforest, Auteur Editeur : Les Ulis : EDP Sciences Année de publication : 2017 Importance : 222 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-2-7598-1830-3 Note générale : Bibliographie Langues : Français (fre) Descripteur : [Vedettes matières IGN] Analyse mathématique
[Termes IGN] algorithmique
[Termes IGN] arbre (mathématique)
[Termes IGN] chemin le plus court, algorithme du
[Termes IGN] graphe
[Termes IGN] théorie des graphesIndex. décimale : 23.30 Analyse mathématique Résumé : (Editeur) Un graphe est un objet abstrait très simple, composé d'éléments (les sommets) et de relations entre ces éléments (les arêtes). Un graphe permet de représenter des liens d'amitié entre des gens, des lignes aériennes entre des villes, des câbles entre des ordinateurs, des références entre des pages web, etc. Ce concept est utilisé dans l'industrie (informatique, recherche opérationnelle) mais il intéresse aussi les chercheurs (étude des réseaux sociaux, biologie, mathématiques...). En s'appuyant sur de multiples exemples et illustrations, ce livre propose une initiation aux graphes et à certaines de leurs propriétés (représentation planaire, cycles eulériens, hamiltoniens...). En évitant tout jargon technique, il décrit des algorithmes classiques (parcours en largeur, en profondeur, Prim, tri topologique, flots...) et d'autres, plus avancés, permettant de traiter les problèmes de coloration, de couverture, d'arbre de Steiner, du voyageur de commerce etc. Cet ouvrage, tout en couleurs, est une invitation à la découverte, sans prérequis, d'un sujet que nul ne devrait ignorer, situé entre les mathématiques discrètes et l'informatique. Note de contenu : 1. Présentation
2. Un graphe. Qu'est-ce que c'est ?
3. Parcourons un graphe en largeur
4. Parcourons un graphe en profondeur
5. Un arbre très léger
6. Construisons un arbre à partir d'une suite de degrés
7. Dessinons un graphe dans le plan sans croiser les arêtes
8. Passons une seule fois par chaque arête
9. Passons une seule fois par chaque sommet
10. Travaillons ensemble
11. Les flots : un problème de plomberie informatique
12. Fabriquons une notice de montage
13. À vous de jouer !
14. Des problèmes très difficiles à résoudre
15. Colorions les graphes
16. Des couplages
17. Une petite couverture
18. Le problème du voyageur de commerce
19. Retour sur l'arbre léger
20. Un arbre couvrant minimisant la somme des distances
21. Découper un graphe en deux grâce à une pièce de monnaie
22. Un avenir incertain
23. Autres problèmes et autres approches
24. Quelques références et complémentsNuméro de notice : 22727 Affiliation des auteurs : non IGN Thématique : INFORMATIQUE/MATHEMATIQUE Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=85362 Réservation
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Titre : Advances in discrete differential geometry Type de document : Monographie Auteurs : Alexander I. Bobenko, Éditeur scientifique Editeur : Berlin, Heidelberg, Vienne, New York, ... : Springer Année de publication : 2016 Importance : 439 p. ISBN/ISSN/EAN : 978-3-662-50447-5 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique
[Termes IGN] géométrie différentielleIndex. décimale : 23.30 Analyse mathématique Résumé : (Editeur) [Preface] In this book we take a closer look at discrete models in differential geometry and dynamical systems. The curves used are polygonal, surfaces are made from triangles and quadrilaterals, and time runs discretely. Nevertheless, one can hardly see the difference to the corresponding smooth curves, surfaces, and classical dynamical systems with continuous time. This is the paradigm of structure-preserving discretizations. The common idea is to find and investigate discrete models that exhibit properties and structures characteristic of the corresponding smooth geometric objects and dynamical processes. These important and characteristic qualitative features should already be captured at the discrete level. The current interest and advances in this field are to a large extent stimulated by its relevance for computer graphics, mathematical physics, architectural geometry, etc. The book focuses on differential geometry and dynamical systems, on smooth and discrete theories, and on pure mathematics and its practical applications. It demonstrates this interplay using a range of examples, which include discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, special texture mappings in computer graphics, and freeform architecture. It was written by specialists from the DFG Collaborative Research Center “Discretization in Geometry and Dynamics”. The work involved in this book and other selected research projects pursued by the Center was recently documented in the film “The Discrete Charm of Geometry” by Ekaterina Eremenko. Lastly, the book features a wealth of illustrations, revealing that this new branch of mathematics is both (literally) beautiful and useful. In particular the cover illustration shows the discretely conformally parametrized surfaces of the inflated letters A and B from the recent educational animated film “conform!” by Alexander Bobenko and Charles Gunn. At this place, we want to thank the Deutsche Forschungsgesellschaft for its ongoing support. Note de contenu :
- Discrete Conformal Maps: Boundary Value Problems, Circle Domains, Fuchsian and Schottky Uniformization /Alexander I. Bobenko, Stefan Sechelmann and Boris Springborn
- Discrete Complex Analysis on Planar Quad-Graphs / Alexander I. Bobenko and Felix Günther
- Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices / Ulrike Bücking
- Numerical Methods for the Discrete Map Za / Folkmar Bornemann, Alexander Its, Sheehan Olver and Georg Wechslberger
- A Variational Principle for Cyclic Polygons with Prescribed EdgeLengths / Hana Kouřimská, Lara Skuppin and Boris Springborn
- Complex Line Bundles Over Simplicial Complexes and Their Applications / Felix Knöppel and Ulrich Pinkall
- Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes / Wai Yeung Lam and Ulrich Pinkall
- Vertex Normals and Face Curvatures of Triangle Meshes / Xiang Sun, Caigui Jiang, Johannes Wallner and Helmut Pottmann
- S-Conical CMC Surfaces. Towards a Unified Theory of Discrete Surfaces with Constant Mean Curvature / Alexander I. Bobenko and Tim Hoffmann
- Constructing Solutions to the Björling Problem for Isothermic Surfaces by Structure Preserving Discretization / Ulrike Bücking and Daniel Matthes
- On the Lagrangian Structure of Integrable Hierarchies /Yuri B. Suris and Mats Vermeeren
- On the Variational Interpretation of the Discrete KP Equation / Raphael Boll, Matteo Petrera and Yuri B. Suris
- Six Topics on Inscribable Polytopes / Arnau Padrol and Günter M. Ziegler
- DGD Gallery: Storage, Sharing, and Publication of Digital Research Data / Michael Joswig, Milan Mehner, Stefan Sechelmann, Jan Techter and Alexander I. BobenkoNuméro de notice : 22744 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Recueil / ouvrage collectif En ligne : http://dx.doi.org/10.1007/978-3-662-50447-5 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=86051 Documents numériques
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22744_Advances in discrete differential geometryAdobe Acrobat PDF
Titre : Quantization on nilpotent lie groups Type de document : Monographie Auteurs : Veronique Fischer, Auteur ; Michael Ruzhansky, Auteur Editeur : Berlin, Zurich, Stuttgart : Birkhaüser Année de publication : 2016 Collection : Progress in Mathematics, ISSN 0743-1643 num. 314 Importance : 557 p. ISBN/ISSN/EAN : 978-3-319-29558-9 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique
[Termes IGN] analyse fonctionnelle (mathématiques)
[Termes IGN] groupe de Lie
[Termes IGN] topologieIndex. décimale : 23.30 Analyse mathématique Résumé : (Auteur) [Preface] The purpose of this monograph is to give an exposition of the global quantization of operators on nilpotent homogeneous Lie groups. We also present the background analysis on homogeneous and graded nilpotent Lie groups. The analysis on homogeneous nilpotent Lie groups drew a considerable attention from the 70’s onwards. Research went in several directions, most notably in harmonic analysis and in the study of hypoellipticity and solvability of partial differential equations. Over the decades the subject has been developing on different levels with advances in the analysis on the Heisenberg group, stratified Lie groups, graded Lie groups, and general homogeneous Lie groups. In the last years analysis on homogeneous Lie groups and also on other types of Lie groups has received another boost with newly found applications and further advances in many topics. Examples of this boost are subelliptic estimates, multiplier theorems, index formulae, nonlinear problems, potential theory, and symbolic calculi tracing full symbols of operators. In particular, the latter has produced further applications in the study of linear and nonlinear partial differential equations, requiring the knowledge of lower order terms of the operators. Because of the current advances, it seems to us that a systematic exposition of the recently developed quantizations on Lie groups is now desirable. This requires bringing together various parts of the theory in the right generality, and extending notions and techniques known in particular cases, for instance on compact Lie groups or on the Heisenberg group. In order to do so, we start with a review of the recent developments in the global quantization on compact Lie groups. In this, we follow mostly the development of this subject in the monograph [RT10a] by Turunen and the second author, as well as its further progress in subsequent papers. After a necessary exposition of the background analysis on graded and homogeneous Lie groups, we present the quantization on general graded Lie groups. As the final part of the monograph, we work out details of the general theory developed in this book in the particular case of the Heisenberg group. In the introduction, we will provide a link between, on one hand, the symbolic calculus of matrix valued symbols on compact Lie groups with, on the other hand, different approaches to the symbolic calculus on the Heisenberg group for instance. We will also motivate further our choices of presentation from the point of view of the development of the theory and of its applications. We would like to thank Fulvio Ricci for discussions and for useful comments on the historical overview of parts of the subject that we tried to present in the introduction. We would also like to thank Gerald Folland for comments leading to improvements of some parts of the monograph. Finally, it is our pleasure to acknowledge the financial support by EPSRC (grant EP/K039407/1), Marie Curie FP7 (Project PseudodiffOperatorS - 301599), and by the Leverhulme Trust (grant RPG-2014-02) at different stages of preparing this monograph. Note de contenu :
Introduction
Notation and conventions
1 Preliminaries on Lie groups
1.1 Lie groups, representations, and Fourier transform
1.2 Liealgebrasandvectorfields
1.3 Universalenvelopingalgebraanddifferentialoperators
1.4 DistributionsandSchwartzkerneltheorem
1.5 Convolutions
1.6 NilpotentLiegroupsandalgebras
1.7 Smooth vectors and infinitesimal representations . .
1.8 Planchereltheorem
2 Quantization on compact Lie groups
2.1 FourieranalysisoncompactLiegroups
2.2 Pseudo-differentialoperatorsoncompactLiegroups
3 Homogeneous Lie groups
3.1 GradedandhomogeneousLiegroups
3.2 OperatorsonhomogeneousLiegroups
4 Rockland operators and Sobolev spaces
4.1 Rocklandoperators
4.2 PositiveRocklandoperators
4.3 FractionalpowersofpositiveRocklandoperators
4.4 SobolevspacesongradedLiegroups
4.5 Hulanicki’s theorem
5 Quantization on graded Lie groups
5.1 Symbolsandquantization
5.2 Symbol classes
5.3 SpectralmultipliersinpositiveRocklandoperators
5.4 Kernelsofpseudo-differentialoperators
5.5 Symboliccalculus
5.6 Amplitudesandamplitudeoperators
5.7 Calderon-Vaillancourt theorem
5.8 Parametrices, ellipticity and hypoellipticity
6 Pseudo-differential operators on the Heisenberg group
6.1 Preliminaries
6.2 DualoftheHeisenberggroup
6.3 Differenceoperators
6.4 Shubin classes
6.5 Quantization and symbol classes on the Heisenberg group
6.6 Parametrices
A Miscellaneous
B Group C∗ and von Neumann algebrasNuméro de notice : 22745 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Monographie En ligne : http://dx.doi.org/10.1007/978-3-319-29558-9 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=86056 Documents numériques
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22745_Quantization on nilpotent lie groupsAdobe Acrobat PDF
Titre : Topological groups : yesterday, today, tomorrow Type de document : Monographie Auteurs : Sidney A. Morris, Éditeur scientifique Editeur : Bâle [Suisse] : Multidisciplinary Digital Publishing Institute MDPI Année de publication : 2016 ISBN/ISSN/EAN : 978-3-03842-269-3 Note générale : Printed edition of the special issue published in Axioms Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique
[Termes IGN] groupe de Lie
[Termes IGN] relation topologique
[Termes IGN] topologieRésumé : (Editeur) In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century. It required half a century of effort by several generations of eminent mathematicians until it was settled in the affirmative. These efforts resulted over time in the Peter-Weyl Theorem, the Pontryagin-van Kampen Duality Theorem for locally compact abelian groups, and finally the solution of Hilbert 5 and the structure theory of locally compact groups, through the combined work of Andrew Gleason, Kenkichi Iwasawa, Deane Montgomery, and Leon Zippin. For a presentation of Hilbert 5 see the 2014 book “Hilbert’s Fifth Problem and Related Topics” by the winner of a 2006 Fields Medal and 2014 Breakthrough Prize in Mathematics, Terence Tao.It is not possible to describe briefly the richness of the topological group theory and the many directions taken since Hilbert 5. The 900 page reference book in 2013 “The Structure of Compact Groups” by Karl H. Hofmann and Sidney A. Morris, deals with one aspect of compact group theory. There are several books on profinite groups including those written by John S. Wilson (1998) and by Luis Ribes and Pavel Zalesskii (2012). The 2007 book “The Lie Theory of Connected Pro-Lie Groups” by Karl Hofmann and Sidney A. Morris, demonstrates how powerful Lie Theory is in exposing the structure of infinite-dimensional Lie groups.The study of free topological groups initiated by A.A. Markov, M.I. Graev and S. Kakutani, has resulted in a wealth of interesting results, in particular those of A.V. Arkhangelʹskiĭ and many of his former students who developed this topic and its relations with topology. The book “Topological Groups and Related Structures” by Alexander Arkhangelʹskii and Mikhail Tkachenko has a diverse content including much material on free topological groups. Compactness conditions in topological groups, especially pseudocompactness as exemplified in the many papers of W.W. Comfort, has been another direction which has proved very fruitful to the present day. Numéro de notice : 22738 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Recueil / ouvrage collectif En ligne : http://www.doabooks.org/doab?func=search&uiLanguage=en&template=&query=TOPOLOGIC [...] Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=85680 Documents numériques
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22738_Topological groupsAdobe Acrobat PDF
Titre : Introduction to partial differential equations Type de document : Guide/Manuel Auteurs : Peter J. Olver, Auteur Editeur : Springer International Publishing Année de publication : 2014 Importance : 636 p. Format : 18 x 26 cm ISBN/ISSN/EAN : 978-3-319-02099-0 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique
[Termes IGN] équation de Laplace
[Termes IGN] équation de Poisson
[Termes IGN] équation différentielle
[Termes IGN] équation linéaire
[Termes IGN] équation non linéaire
[Termes IGN] équation polynomiale
[Termes IGN] fonction de Green
[Termes IGN] principe de Huygens
[Termes IGN] transformation de Fourier
[Termes IGN] valeur limiteRésumé : (auteur) This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject.
No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens'
Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.Note de contenu : 1- What Are Partial Differential Equations?
2- Linear and Nonlinear Waves
3- Fourier Series
4- Separation of Variables
5- Finite Differences
6- Generalized Functions and Green’s Functions
7- Fourier Transforms
8- Linear and Nonlinear Evolution Equations
9- A General Framework for Linear Partial Differential Equations
10- Finite Elements and Weak Solutions
11- Dynamics of Planar Media
12- Partial Differential Equations in SpaceNuméro de notice : 25874 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel DOI : 10.1007/978-3-319-02099-0 En ligne : https://doi.org/10.1007/978-3-319-02099-0 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95568 Généralisation du diagramme de Voronoï et placement de formes géométriques complexes dans un nuage de points / Thomas Iwaszko (2012)
PermalinkPermalinkPermalinkDeveloping an adaptive topological tessellation for 3D modeling in geosciences / L. Hashemi Beni in Geomatica, vol 63 n° 4 (December 2009)
PermalinkPermalinkPermalinkPermalinkPermalinkPermalinkComparaison de trois familles d'ondelettes pour la représentation du champ de pesanteur terrestre / Isabelle Panet (2003)
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