An algebraic approach to physical scales
type: Item
instance of: scholarly article
title: An algebraic approach to physical scales
zbMATH Open document ID: 1208.15021
author: Josef Janyška
author: Marco Modugno
author: Raffaele Vitolo
published in: Acta Applicandae Mathematicae
publication date: 2010-05-19T00:00:00Z
review text: The authors propose the category of positive spaces (i.e. essentially the \(1\)-dimensional semi-vector spaces over \(\mathbb R^{+}\)) and \(q\)-rational maps (for all \(q \in Q\)) between them, as a convenient mathematical setting to formulate the intuitive notions of physical scales and units of measurement. To this end, semi-tensor products, spaces of morphisms and rational powers of a positive space are treated. Besides, using methods of Differential Geometry, the bundles of positive spaces based on spacetime and their semi-linear connections are discussed. A brief review of the relationship to dimensional analysis is also given [e.g., see \textit{G. I. Barenblatt}, Scaling. Cambridge Texts in Applied Mathematics. Cambridge: Cambridge University Press (2003; Zbl 1094.00006)].
reviewed by: George F. Nassopoulos
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 12K10
Mathematics Subject Classification ID: 16Y60
Mathematics Subject Classification ID: 70S99
zbMATH DE Number: 5709144
zbMATH Keywords: semi-vector spaces
zbMATH Keywords: scales
zbMATH Keywords: units of measurement
zbMATH Keywords: \(q\)-rational maps
zbMATH Keywords: semi-tensor products
zbMATH Keywords: spaces of morphisms
zbMATH Keywords: bundles of positive spaces
zbMATH Keywords: semi-linear connections
MaRDI profile type: Publication
full work available at URL: s10440-009-9505-6
OpenAlex ID: W2097924062
Wikidata QID: Q57555706
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DOI: 10.1007/S10440-009-9505-6
description: scientific article; zbMATH DE number 5709144