國立虎尾科技大學 |

Encyclopedia of distances

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Encyclopedia of distances/ by Michel Marie Deza, Elena Deza.
Author:	Deza, Michel Marie.
other author:	Deza, Elena.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2016.,
Description:	xxii, 756 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Metric spaces. -
Online resource:	http://dx.doi.org/10.1007/978-3-662-52844-0
ISBN:	9783662528440

Encyclopedia of distances
Deza, Michel Marie.

Encyclopedia of distances[electronic resource] /by Michel Marie Deza, Elena Deza. - 4th ed. - Berlin, Heidelberg :Springer Berlin Heidelberg :2016. - xxii, 756 p. :ill., digital ;24 cm.

Part I. Mathematics of Distances: 1 General Definitions -- 2 Topological Spaces -- 3 Generalization of Metric Spaces -- 4 Metric Transforms -- 5 Metrics on Normed Structures -- Part II. Geometry and Distances: 6 Distances in Geometry -- 7 Riemannian and Hermitian Metrics -- 8 Distances on Surfaces and Knots -- 9 Distances on Convex Bodies, Cones and Simplicial Complexes -- Part III. Distances in Classical Mathematics: 10 Distances in Algebra -- 11 Distances on Strings and Permutations -- 12 Distances on Numbers, Polynomials and Matrices -- 13 Distances in Functional Analysis -- 14 Distances in Probability Theory -- Part IV. Distances in Applied Mathematics: 15 Distances in Graph Theory -- 16 Distances in Coding Theory -- 17 Distances and Similarities in Data Analysis -- 18 Distances in Systems and Mathematical Engineering -- Part V. Computer-Related Distances: 19 Distances on Real and Digital Planes -- 20 Voronoi Diagram Distances -- 21 Image and Audio Distances -- 22 Distances in Networks -- Part VI. Distances in Natural Sciences: 23 Distances in Biology -- 24 Distances in Physics and Chemistry -- 25 Distances in Earth Science and Astronomy -- 26 Distances in Cosmology and Theory of Relativity -- Part VII. Real-World Distances: 27 Length Measures and Scales -- 28 Distances in Applied Social Sciences -- 29 Other Distances.

This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis. New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance. Leaving aside the practical questions that arise during the selection of a ‘good' distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who's Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.

ISBN: 9783662528440

Standard No.: 10.1007/978-3-662-52844-0doiSubjects--Topical Terms:

527849
Metric spaces.

LC Class. No.: QA611.28 / .D49 2016

Dewey Class. No.: 514.325

Encyclopedia of distances
LDR:04215nam a2200325 a 4500 001 866573
003 DE-He213
005 20170218113218.0
006 m d
007 cr nn 008maaau
008 170720s2016 gw s 0 eng d
020 $a 9783662528440 $q (electronic bk.)
020 $a 9783662528433 $q (paper)
024 7 $a 10.1007/978-3-662-52844-0 $2 doi
035 $a 978-3-662-52844-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA611.28 $b .D49 2016
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
082 0 4 $a 514.325 $2 23
090 $a QA611.28 $b .D532 2016
100 1 $a Deza, Michel Marie. $3 898667
245 1 0 $a Encyclopedia of distances $h [electronic resource] / $c by Michel Marie Deza, Elena Deza.
250 $a 4th ed.
260 $a Berlin, Heidelberg : $c 2016. $b Springer Berlin Heidelberg : $b Imprint: Springer,
300 $a xxii, 756 p. : $b ill., digital ; $c 24 cm.
505 0 $a Part I. Mathematics of Distances: 1 General Definitions -- 2 Topological Spaces -- 3 Generalization of Metric Spaces -- 4 Metric Transforms -- 5 Metrics on Normed Structures -- Part II. Geometry and Distances: 6 Distances in Geometry -- 7 Riemannian and Hermitian Metrics -- 8 Distances on Surfaces and Knots -- 9 Distances on Convex Bodies, Cones and Simplicial Complexes -- Part III. Distances in Classical Mathematics: 10 Distances in Algebra -- 11 Distances on Strings and Permutations -- 12 Distances on Numbers, Polynomials and Matrices -- 13 Distances in Functional Analysis -- 14 Distances in Probability Theory -- Part IV. Distances in Applied Mathematics: 15 Distances in Graph Theory -- 16 Distances in Coding Theory -- 17 Distances and Similarities in Data Analysis -- 18 Distances in Systems and Mathematical Engineering -- Part V. Computer-Related Distances: 19 Distances on Real and Digital Planes -- 20 Voronoi Diagram Distances -- 21 Image and Audio Distances -- 22 Distances in Networks -- Part VI. Distances in Natural Sciences: 23 Distances in Biology -- 24 Distances in Physics and Chemistry -- 25 Distances in Earth Science and Astronomy -- 26 Distances in Cosmology and Theory of Relativity -- Part VII. Real-World Distances: 27 Length Measures and Scales -- 28 Distances in Applied Social Sciences -- 29 Other Distances.
520 $a This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis. New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance. Leaving aside the practical questions that arise during the selection of a ‘good' distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who's Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.
650 0 $a Metric spaces. $3 527849
650 0 $a Distances $x Measurement. $3 1072525
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Topology. $3 633483
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 669338
650 2 4 $a Appl.Mathematics/Computational Methods of Engineering. $3 669335
700 1 $a Deza, Elena. $3 857653
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-662-52844-0
950 $a Mathematics and Statistics (Springer-11649)