On scientific laws without dimensional constants
type: Item
instance of: scholarly article
title: On scientific laws without dimensional constants
zbMATH Open document ID: 0605.39004
DOI: 10.1016/0022-247X(86)90162-9
author: János Aczél
author: Fred Roberts
author: Zangwill Rosenbaum
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The authors consider twelve functional equations of several variables arising from assumptions of various scale types for the independent and dependent variables, and without necessarily assuming that all these admissible transformations can be applied independently to all of the independent variables. The motivation for this investigation is one of possible ''general forms'' for ''scientific laws''. Some of the equations discussed were discussed by various people under more restrictive assumptions, in particular R. D. Luce (who assumed, for example, the independence of the application of the admissible transformations). As a consequence, the resulting solutions in the authors' treatment are not as restrictively specified as they were in earlier ones, and so more general ''laws'' than linear or constant ones emerge. Especially in cases 7-12 treated in the paper, in which there are interval scales for the independent variables, nevertheless the general solutions turn out to have very special forms. The authors in all cases indicate how various regularity conditions restrict the set of solutions, thus recapturing the results of previous studies of equations as well.
Mathematics Subject Classification ID: 39B99
Mathematics Subject Classification ID: 15A90
zbMATH DE Number: 3977572
zbMATH Keywords: scientific law
zbMATH Keywords: admissible transformations
zbMATH Keywords: independent variables
zbMATH Keywords: general form
reviewed by: Sanford L. Segal
MaRDI profile type: Publication
cites work: Q5514010
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full work available at URL: 0022-247x(86)90162-9
OpenAlex ID: W2070861039
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description: scientific article; zbMATH DE number 3977572