Encyclopedia of Distances

Description

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.