Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Branch_point> ?p ?o }
- Branch_point abstract "In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point. Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept.Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation z = w2 for w as a function of z. Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function: there is non-trivial monodromy. Despite the algebraic branch point, the function w is well-defined as a multiple-valued function and, in an appropriate sense, is continuous at the origin. This is in contrast to transcendental and logarithmic branch points, that is, points at which a multiple-valued function has nontrivial monodromy and an essential singularity. In geometric function theory, unqualified use of the term branch point typically means the former more restrictive kind: the algebraic branch points. In other areas of complex analysis, the unqualified term may also refer to the more general branch points of transcendental type.".
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- Branch_point wikiPageWikiLink File:Riemann_surface_log.svg.
- Branch_point wikiPageWikiLinkText "Branch cuts".
- Branch_point wikiPageWikiLinkText "Branch point".
- Branch_point wikiPageWikiLinkText "branch cuts".
- Branch_point wikiPageWikiLinkText "branch point".
- Branch_point wikiPageWikiLinkText "branch point#Branch cuts".
- Branch_point wikiPageWikiLinkText "branch".
- Branch_point wikiPageWikiLinkText "branches".
- Branch_point first "E.D.".
- Branch_point hasPhotoCollection Branch_point.
- Branch_point id "B/b017500".
- Branch_point last "Solomentsev".
- Branch_point title "Branch point".
- Branch_point wikiPageUsesTemplate Template:Citation.
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- Branch_point year "2001".
- Branch_point subject Category:Complex_analysis.
- Branch_point subject Category:Inverse_functions.
- Branch_point hypernym Point.
- Branch_point type Article.
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- Branch_point type Type.
- Branch_point type Article.
- Branch_point type Function.
- Branch_point type Type.
- Branch_point comment "In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.".
- Branch_point label "Branch point".
- Branch_point sameAs Point_de_branchement.
- Branch_point sameAs 分岐点_(数学).
- Branch_point sameAs Тармақталу_нүктесі.
- Branch_point sameAs Puunt_da_desbrancameent.
- Branch_point sameAs Vertakkingspunt.
- Branch_point sameAs Punkt_rozgałęzienia.
- Branch_point sameAs Ponto_de_ramificação.
- Branch_point sameAs m.02fxkj.
- Branch_point sameAs Точка_ветвления.
- Branch_point sameAs Точка_розгалуження.
- Branch_point sameAs Q2625091.