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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 a Raffaele VITOLO. An algebraic approach to physical scales. \textit{Acta Applicandae Mathematicae}. Kluwer, 2010, roč.~110, č.~3, s.~1249-1276. ISSN~0167-8019.
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