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Mathematical structure of unit systems
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10.1063/1.4802876
By Masao Kitano1,a)
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Affiliations:
1 Department of Electronic Science and Engineering, Kyoto University, Katsura, Kyoto 615-8510, Japan
a) Electronic mail: kitano@kuee.kyoyo-u.ac.jp
J. Math. Phys. 54, 052901 (2013)
/content/aip/journal/jmp/54/5/10.1063/1.4802876
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/5/10.1063/1.4802876

## Figures

FIG. 1.

Ordering of unit systems and . A quantity is mapped to and for the representation in the respective unit systems. In the case of , the preimage is always included in . Only then we can naturally define the mapping .

FIG. 2.

Two equivalence classes of unit systems (EUS's) satisfying , with the mapping . Each EUS contains equivalent unit systems as , . There are invertible mappings between any pair of unit systems in an EUS, for example, and between and . There is a (one-way) mapping from any unit system in to any unit system in . These mappings ( and in this example) are related as . Note that there are also mappings between and ′ ( ) or and ( ), which is not shown here.

FIG. 3.

A hierarchical tree of unit systems. Here, is the number of base units. Arrows indicate transferability “≻,” and the associated quantity is considered to be unity on the transfer. Dashed boxes represent EUS's, and the four- and two-base unit systems listed are equivalent within each group, whereas the three-base unit systems are all incomparable.

## Tables

Table I.

Four possible relations between two unit systems and : (strictly) transferable to (≻), (strictly) transferable from (≺), equivalent (∼), and incomparable (∥). The relations between and , which are the numbers of base units, are also listed.

/content/aip/journal/jmp/54/5/10.1063/1.4802876
2013-05-03
2014-04-19

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