http://qudt.org/schema/qudt/QuantityKindDimensionVector
$\text{Quantity Kind Dimension Vector}$ describes the dimensionality of a quantity kind in the context of a system of units.
In the SI system of units, the dimensions of a quantity kind are expressed as a product of the basic
physical dimensions mass ($M$), length ($L$), time ($T$) current ($I$), amount of substance ($N$),
luminous intensity ($J$) and absolute temperature
($\theta$) as $dim \, Q = L^{\alpha} \, M^{\beta} \, T^{\gamma} \, I ^{\delta} \, \theta ^{\epsilon} \, N^{\eta} \, J ^{\nu}$.
The rational powers of the dimensional exponents, $\alpha, \, \beta, \, \gamma, \, \delta, \, \epsilon, \, \eta, \, \nu$, are positive, negative, or zero.
For example, the dimension of the physical quantity kind $\it{speed}$ is $\boxed{length/time}$, $L/T$ or $LT^{-1}$,
and the dimension of the physical quantity kind force is $\boxed{mass \times acceleration}$ or $\boxed{mass \times (length/time)/time}$, $ML/T^2$ or $MLT^{-2}$ respectively.
Focus nodes of this shape (qudt:QuantityKindDimensionVector) can have the following properties:
| PROPERTY | DESCRIPTION | MIN | MAX | VALUE TYPE | OTHER CONSTRAINTS |
|---|---|---|---|---|---|
| qudt:dimensionExponentForAmountOfSubstance | 1 | 1 | |||
| qudt:dimensionExponentForElectricCurrent | 1 | 1 | xsd:integer | ||
| qudt:dimensionExponentForLength | 1 | 1 | |||
| qudt:dimensionExponentForLuminousIntensity | 1 | 1 | |||
| qudt:dimensionExponentForMass | 1 | 1 | |||
| qudt:dimensionExponentForThermodynamicTemperature | 1 | 1 | |||
| qudt:dimensionExponentForTime | 1 | 1 | |||
| qudt:dimensionlessExponent | 1 | 1 | |||
| qudt:hasReferenceQuantityKind | 0 | * | qudt:QuantityKind | ||
| qudt:latexDefinition | 0 | 1 | qudt:LatexString | ||
| qudt:latexSymbol | The symbol is a glyph that is used to represent some concept, typically a unit or a quantity, in a compact form. For example, the symbol for an Ohm is $ohm$. This contrasts with 'unit:abbreviation', which gives a short alphanumeric abbreviation for the unit, 'ohm' for Ohm. | 0 | * | qudt:LatexString |
@prefix dcterms: <http://purl.org/dc/terms/> .
@prefix qudt: <http://qudt.org/schema/qudt/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix sh: <http://www.w3.org/ns/shacl#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
qudt:QuantityKindDimensionVector a rdfs:Class,
sh:NodeShape ;
rdfs:label "Quantity Kind Dimension Vector" ;
dcterms:description """
$\\text{Quantity Kind Dimension Vector}$ describes the dimensionality of a quantity kind in the context of a system of units.
In the SI system of units, the dimensions of a quantity kind are expressed as a product of the basic
physical dimensions mass ($M$), length ($L$), time ($T$) current ($I$), amount of substance ($N$),
luminous intensity ($J$) and absolute temperature
($\\theta$) as $dim \\, Q = L^{\\alpha} \\, M^{\\beta} \\, T^{\\gamma} \\, I ^{\\delta} \\, \\theta ^{\\epsilon} \\, N^{\\eta} \\, J ^{\\nu}$.
The rational powers of the dimensional exponents, $\\alpha, \\, \\beta, \\, \\gamma, \\, \\delta, \\, \\epsilon, \\, \\eta, \\, \\nu$, are positive, negative, or zero.
For example, the dimension of the physical quantity kind $\\it{speed}$ is $\\boxed{length/time}$, $L/T$ or $LT^{-1}$,
and the dimension of the physical quantity kind force is $\\boxed{mass \\times acceleration}$ or $\\boxed{mass \\times (length/time)/time}$, $ML/T^2$ or $MLT^{-2}$ respectively.
"""^^qudt:LatexString ;
qudt:informativeReference "http://web.mit.edu/2.25/www/pdf/DA_unified.pdf"^^xsd:anyURI,
"https://en.wikipedia.org/wiki/Dimensional_analysis"^^xsd:anyURI ;
rdfs:isDefinedBy <http://qudt.org/3.5.2/schema/shacl/qudt> ;
rdfs:subClassOf qudt:Concept ;
sh:property qudt:QuantityKindDimensionVector-dimensionExponentForAmountOfSubstance,
qudt:QuantityKindDimensionVector-dimensionExponentForElectricCurrent,
qudt:QuantityKindDimensionVector-dimensionExponentForLength,
qudt:QuantityKindDimensionVector-dimensionExponentForLuminousIntensity,
qudt:QuantityKindDimensionVector-dimensionExponentForMass,
qudt:QuantityKindDimensionVector-dimensionExponentForThermodynamicTemperature,
qudt:QuantityKindDimensionVector-dimensionExponentForTime,
qudt:QuantityKindDimensionVector-dimensionlessExponent,
qudt:QuantityKindDimensionVector-hasReferenceQuantityKind,
qudt:QuantityKindDimensionVector-latexDefinition,
qudt:QuantityKindDimensionVector-latexSymbol .