On scientific laws without dimensional constants
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.
scientific article; zbMATH DE number 3977572