Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Kelvin_transform> ?p ?o. }
Showing items 1 to 20 of
20
with 100 items per page.
- Kelvin_transform abstract "This article is about a type of transform used in classical potential theory, a topic in mathematics. The Kelvin transform is a device used in classical potential theory to extend the concept of a harmonic function, by allowing the definition of a function which is 'harmonic at infinity'. This technique is also used in the study of subharmonic and superharmonic functions.In order to define the Kelvin transform f* of a function f, it is necessary to first consider the concept of inversion in a sphere in Rn as follows.It is possible to use inversion in any sphere, but the ideas are clearest when considering a sphere with centre at the origin.Given a fixed sphere S(0,R) with centre 0 and radius R, the inversion of a point x in Rn is defined to beA useful effect of this inversion is that the origin 0 is the image of , and is the image of 0. Under this inversion, spheres are transformed into spheres, and the exterior of a sphere is transformed to the interior, and vice versa.The Kelvin transform of a function is then defined by:If D is an open subset of Rn which does not contain 0, then for any function f defined on D, the Kelvin transform f* of f with respect to the sphere S(0,R) isOne of the important properties of the Kelvin transform, and the main reason behind its creation, is the following result:Let D be an open subset in Rn which does not contain the origin 0. Then a function u is harmonic, subharmonic or superharmonic in D if and only if the Kelvin transform u* with respect to the sphere S(0,R) is harmonic, subharmonic or superharmonic in D*.This follows from the formula".
- Kelvin_transform wikiPageID "6000460".
- Kelvin_transform wikiPageRevisionID "544467039".
- Kelvin_transform hasPhotoCollection Kelvin_transform.
- Kelvin_transform subject Category:Harmonic_functions.
- Kelvin_transform subject Category:Transforms.
- Kelvin_transform type Abstraction100002137.
- Kelvin_transform type Function113783816.
- Kelvin_transform type HarmonicFunctions.
- Kelvin_transform type MathematicalRelation113783581.
- Kelvin_transform type Relation100031921.
- Kelvin_transform comment "This article is about a type of transform used in classical potential theory, a topic in mathematics. The Kelvin transform is a device used in classical potential theory to extend the concept of a harmonic function, by allowing the definition of a function which is 'harmonic at infinity'.".
- Kelvin_transform label "Kelvin transform".
- Kelvin_transform label "Преобразование Кельвина".
- Kelvin_transform sameAs m.0fj_9f.
- Kelvin_transform sameAs Q4377358.
- Kelvin_transform sameAs Q4377358.
- Kelvin_transform sameAs Kelvin_transform.
- Kelvin_transform wasDerivedFrom Kelvin_transform?oldid=544467039.
- Kelvin_transform isPrimaryTopicOf Kelvin_transform.