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Abel transform

In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by

Geometrical interpretation, Generalization of the Abel transform to discontinuous F(y) & Relationship to other integral transforms

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Geometrical interpretation

Symmetric functionRadiusEven functionWithout loss of generalityAxial symmetry
5 related topics

Generalization of the Abel transform to discontinuous F(y)

Polymer brushPhase separationDirac delta functionHeaviside step function
4 related topics

Relationship to other integral transforms

Projection-slice theoremFourier transformHankel transformRadon transform
4 related topics

Verification of the inverse Abel transform

FormallyFubini's theorem
2 related topics

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Overview

Geometrical interpretation

Verification of the inverse Abel transform

Generalization of the Abel transform to discontinuous F(y)

Relationship to other integral transforms

Advanced semantic analysis

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Abel transform

Nodes30
Edges29
Triples20
Avg. degree1.93
Density0.066667
Components1

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Abel transform

Top relations

related to Relationship to the Fourier and Hankel transforms · 8
Abel transform → Abel, FHA, For, Fourier, Hankel, In, The Abel, This
related to Geometrical interpretation · 5
Abel transform → Abel, In, It, Realizing, Referring
related to Relationship to the Radon transform · 4
Abel transform → Abel, As, Radon, Thus
is a · 2
Abel transform → function of the distance along the viewing axis only, integrated absorbance along a ray with closest distance y from the center of the flame

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Important terminology

transform abel function inverse symmetric analysis axially integral dimensions plane projection circularly axis y2 assuming zero onto along distance used

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Abel transformis aintegrated absorbance along a ray with closest distance y from the center of the flame0.90text
Abel transformis afunction of the distance along the viewing axis only0.90text
algebraic reconstruction techniqueinstance ofmore general-oriented reconstruction algorithms0.80text
Abel transformrelated to Geometrical interpretationIn0.60section
Abel transformrelated to Geometrical interpretationAbel0.60section
Abel transformrelated to Geometrical interpretationReferring0.60section
Abel transformrelated to Geometrical interpretationIt0.60section
Abel transformrelated to Geometrical interpretationRealizing0.60section
Abel transformrelated to Relationship to the Fourier and Hankel transformsThe Abel0.60section
Abel transformrelated to Relationship to the Fourier and Hankel transformsFHA0.60section
Abel transformrelated to Relationship to the Fourier and Hankel transformsFor0.60section
Abel transformrelated to Relationship to the Fourier and Hankel transformsAbel0.60section

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