Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Deza, Michel Marie
Titre(s) : Encyclopedia of Distances [Texte électronique]
Titre d'ensemble : Encyclopedia of distances / Deza, Michel.
Édition : 3rd ed (Online-Ausg.)
Publication : Berlin, Heidelberg : Springer Berlin Heidelberg, 2014
Description matérielle : Online-Ressource (1 online resource (731 p.))
Collection : EBL-Schweitzer
Note(s) : Description based upon print version of record. - 22.1 Scale-Free Networks
Preface; Preface to the Second Edition; Preface to the First Edition; Preface to Dictionary
of Distances, 2006; Contents; Part I Mathematics of Distances; 1 General Definitions
; 1.1 Basic Definitions; 1.2 Main Distance-Related Notions; 1.3 Metric Numerical Invariants;
1.4 Main Mappings of Metric Spaces; 1.5 General Distances; 2 Topological Spaces; 3
Generalizations of Metric Spaces; 3.1 m-Tuple Generalizations of Metrics; 3.2 Indefinite
Metrics; 3.3 Topological Generalizations; 3.4 Beyond Numbers; 4 Metric Transforms;
4.1 Metrics on the Same Set; 4.2 Metrics on Set Extensions ; 4.3 Metrics on Other
Sets5 Metrics on Normed Structures ; Part II Geometry and Distances; 6 Distances in
Geometry ; 6.1 Geodesic Geometry; 6.2 Projective Geometry; 6.3 Affine Geometry; 6.4
Non-Euclidean Geometry; 7 Riemannian and Hermitian Metrics; 7.1 Riemannian Metrics
and Generalizations; 7.2 Riemannian Metrics in Information Theory; 7.3 Hermitian Metrics
and Generalizations; 8 Distances on Surfaces and Knots ; 8.1 General Surface Metrics;
8.2 Intrinsic Metrics on Surfaces; 8.3 Distances on Knots; 9 Distances on Convex Bodies,
Cones, and Simplicial Complexes; 9.1 Distances on Convex Bodies ; 9.2 Distances on
Cones9.3 Distances on Simplicial Complexes; Part III Distances in Classical Mathematics;
10 Distances in Algebra; 10.1 Group Metrics; 10.2 Metrics on Binary Relations; 10.3
Metrics on Semilattices; 11 Distances on Strings and Permutations ; 11.1 Distances
on General Strings; 11.2 Distances on Permutations; 12 Distances on Numbers, Polynomials,
and Matrices; 12.1 Metrics on Numbers; 12.2 Metrics on Polynomials; 12.3 Metrics on
Matrices; 13 Distances in Functional Analysis ; 13.1 Metrics on Function Spaces; 13.2
Metrics on Linear Operators; 14 Distances in Probability Theory ; 14.1 Distances on
Random Variables14.2 Distances on Distribution Laws; Part IV Distances in Applied
Mathematics; 15 Distances in Graph Theory; 15.1 Distances on the Vertices of a Graph;
15.2 Distance-Defined Graphs; 15.3 Distances on Graphs; 15.4 Distances on Trees; 16
Distances in Coding Theory; 16.1 Minimum Distance and Relatives; 16.2 Main Coding
Distances; 17 Distances and Similarities in Data Analysis; 17.1 Similarities and Distances
for Numerical Data; 17.2 Relatives of Euclidean Distance; 17.3 Similarities and Distances
for Binary Data; 17.4 Correlation Similarities and Distances ; 18 Distances in Systems
and Mathematical Engineering18.1 Distances in State Transition and Dynamical Systems;
18.2 Distances in Control Theory; 18.3 Motion Planning Distances; 18.4 MOEA Distances;
Part V Computer-Related Distances; 19 Distances on Real and Digital Planes; 19.1 Metrics
on Real Plane; 19.2 Digital Metrics; 20 Voronoi Diagram Distances; 20.1 Classical
Voronoi Generation Distances; 20.2 Plane Voronoi Generation Distances; 20.3 Other
Voronoi Generation Distances; 21 Image and Audio Distances; 21.1 Image Distances;
21.2 Audio Distances; 22 Distances in Networks ; This updated and revised third edition
of the leading reference volume on distance metrics includes new items from very active
research areas in the use of distances and metrics such as geometry, graph theory,
probability theory and analysis. Among the new topics included are, for example, polyhedral
metric space, nearness matrix problems, distances between belief assignments, distance-related
animal settings, diamond-cutting distances, natural units of length, Heidegger's de-severance
distance, and brain distances. The publication of this volume coincides with intensifying
research efforts
Autre(s) auteur(s) : Deza, Elena. Fonction indéterminée
Sujet(s) : Informatique -- Mathématiques
Visualisation
Géométrie différentielle globale
Topologie
Mathématiques de l'ingénieur
Mathématiques
Indice(s) Dewey :
004 (23e éd.) = Informatique
Identifiants, prix et caractéristiques : ISBN 9783662443422
Identifiant de la notice : ark:/12148/cb44713183z
Notice n° :
FRBNF44713183
(notice reprise d'un réservoir extérieur)
