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020 _a9783662443422
_9978-3-662-44342-2
024 7 _a10.1007/978-3-662-44342-2
_2doi
035 _ato000545513
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aDeza, Michel Marie.
_eauthor.
_9453255
245 1 0 _aEncyclopedia of Distances
_helectronic resource
_cby Michel Marie Deza, Elena Deza.
250 _a3rd ed. 2014.
260 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2014.
300 _aXX, 733 p. 3 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _aPart 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 _aThis 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 into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval. 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 _amathematics.
_9566183
650 0 _aComputer science
_xMathematics.
_9304486
650 0 _aVisualization.
_9303600
650 0 _aGeometry.
_9303683
650 0 _aGlobal differential geometry.
_9566343
650 0 _aTopology.
_9303685
650 0 _aEngineering mathematics.
_9303575
650 1 4 _aMathematics.
_9566184
650 2 4 _aGeometry.
_9303683
650 2 4 _aDifferential Geometry.
_9566344
650 2 4 _aTopology.
_9303685
650 2 4 _aComputational Mathematics and Numerical Analysis.
_9303505
650 2 4 _aVisualization.
_9303600
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
_9303577
700 1 _aDeza, Elena.
_eauthor.
_9453256
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-662-44342-2
912 _aZDB-2-SMA
999 _c402902