Distribution of directional data and fabric tensors
type: Item
instance of: scholarly article
title: Distribution of directional data and fabric tensors
zbMATH Open document ID: 0586.73004
DOI: 10.1016/0020-7225(84)90090-9
published in: International Journal of Engineering Science
publication date: 1984-01-01T00:00:00Z
review text: Distribution of directional data is characterized by what is termed fabric tensors. A formal least square approximation is applied, and three kinds of fabric tensors are defined in connection with the choice of a basis of the space of functions on a unit sphere or a unit circle. All the resulting equations are Cartesian tensor equations, and they are interpreted in terms of the representation theory of the rotation group and the potential theory in electrodynamics. It is also shown how this characterization is related to the spherical harmonics expansion or the Fourier series expansion. Finally, a method of statistical test is presented in the Cartesian tensor form to check the true form of the distribution. A physical example is also given to illustrate the proposed technique.
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 53A45
zbMATH DE Number: 3940794
zbMATH Keywords: tensors of second kind
zbMATH Keywords: third kind
zbMATH Keywords: Laplace harmonics
zbMATH Keywords: distribution of directional data
zbMATH Keywords: Fisher information matrix
zbMATH Keywords: fabric tensors
zbMATH Keywords: least square approximation
zbMATH Keywords: Cartesian tensor equations
zbMATH Keywords: representation theory of the rotation group
zbMATH Keywords: potential theory in electrodynamics
zbMATH Keywords: spherical harmonics expansion
zbMATH Keywords: Fourier series expansion
zbMATH Keywords: method of statistical test
author: Ken-Ichi Kanatani
MaRDI profile type: Publication
full work available at URL: 0020-7225(84)90090-9
OpenAlex ID: W2001450167
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description: scientific article; zbMATH DE number 3940794