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@article{882900,
author = {Janyška, Josef and Modugno, Marco and Vitolo, Raffaele},
article_number = {3},
keywords = {semi-vector spaces; scales; units of measurement},
language = {eng},
issn = {0167-8019},
journal = {Acta Applicandae Mathematicae},
title = {An algebraic approach to physical scales},
url = {http://www.springerlink.com/content/100230/?Content+Status=Accepted&sort=p_OnlineDate&sortorder=desc&v=condensed},
volume = {110},
year = {2010}
}
TY - JOUR
ID - 882900
AU - Janyška, Josef - Modugno, Marco - Vitolo, Raffaele
PY - 2010
TI - An algebraic approach to physical scales
JF - Acta Applicandae Mathematicae
VL - 110
IS - 3
SP - 1249-1276
EP - 1249-1276
PB - Kluwer
SN - 01678019
KW - semi-vector spaces
KW - scales
KW - units of measurement
UR - http://www.springerlink.com/content/100230/?Content+Status=Accepted&sort=p_OnlineDate&sortorder=desc&v=condensed
N2 - This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space" and its rational powers. Positive spaces are ``semi--vector spaces'' on which the group of positive real numbers acts freely and transitively through the scalar multiplication. Their tensor multiplication with vector spaces yields ``scaled spaces'' that are suitable to describe spaces with physical dimensions mathematically. We also deal with scales regarded as fields over a given background e.g., spacetime.
ER -
JANYŠKA, Josef, Marco MODUGNO and Raffaele VITOLO. An algebraic approach to physical scales. \textit{Acta Applicandae Mathematicae}. Kluwer, 2010, vol.~110, No~3, p.~1249-1276. ISSN~0167-8019.
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