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.
Instances of qudt:QuantityKindDimensionVector can have the following properties:
| PROPERTY | TYPE | DESCRIPTION | RANGE |
|---|
By the associated SHACL property shapes, instances of qudt:QuantityKindDimensionVector can have the following properties:
| PROPERTY | PROPERTY TYPE | DESCRIPTION | MIN | MAX | VALUE TYPE | OTHER CONSTRAINTS | GLOBAL RANGE |
|---|---|---|---|---|---|---|---|
| qudt:QuantityKindDimensionVector | |||||||
| qudt:dimensionExponentForAmountOfSubstance | rdf:Property | 1 | 1 | -- | |||
| qudt:dimensionExponentForElectricCurrent | rdf:Property | 1 | 1 | xsd:integer | -- | ||
| qudt:dimensionExponentForLength | rdf:Property | 1 | 1 | -- | |||
| qudt:dimensionExponentForLuminousIntensity | rdf:Property | 1 | 1 | -- | |||
| qudt:dimensionExponentForMass | rdf:Property | 1 | 1 | -- | |||
| qudt:dimensionExponentForThermodynamicTemperature | rdf:Property | 1 | 1 | -- | |||
| qudt:dimensionExponentForTime | rdf:Property | 1 | 1 | -- | |||
| qudt:dimensionlessExponent | rdf:Property | 1 | 1 | -- | |||
| qudt:hasReferenceQuantityKind | rdf:Property | 0 | * | qudt:QuantityKind | -- | ||
| qudt:latexDefinition | rdf:Property | 0 | 1 | qudt:LatexString | -- | ||
| qudt:latexSymbol | rdf:Property | 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 | -- | |
| qudt:Concept | |||||||
| dcterms:description | rdf:Property | 0 | * | -- | |||
| dcterms:isReplacedBy | rdf:Property | 0 | 1 | -- | |||
dtype:code |
-- | 0 | * | -- | |||
| qudt:abbreviation | rdf:Property | <p>An abbreviation for a unit is a short ASCII string that is used in place of the full name for the unit in contexts where non-ASCII characters would be problematic, or where using the abbreviation will enhance readability. When a power of abase unit needs to be expressed, such as squares this can be done using abbreviations rather than symbols. For example, <em>sq ft</em> means <em>square foot</em>, and <em>cu ft</em> means <em>cubic foot</em>. </p> | 0 | 1 | xsd:string | -- | |
| qudt:deprecated | rdf:Property | 0 | 1 | xsd:boolean | -- | ||
| qudt:deprecatedInVersion | rdf:Property | Version number of the first QUDT release in which an entity was deprecated. | 0 | 1 | xsd:string |
sh:pattern
^\d+\.\d+\.\d+$
|
-- |
| qudt:exactMatch | owl:ObjectProperty | 0 | * | qudt:Concept | -- | ||
| qudt:guidance | rdf:Property | 0 | * | rdf:HTML | -- | ||
| qudt:hasRule | rdf:Property | 0 | * | qudt:Rule | -- | ||
| qudt:id | rdf:Property | <p>The "qudt:id" is an identifier string that uniquely identifies a QUDT concept. The identifier is constructed using a prefix. For example, units are coded using the pattern: "UCCCENNNN", where "CCC" is a numeric code or a category and "NNNN" is a digit string for a member element of that category. </p> <p>For scaled units there may be an addition field that has the format "QNN" where "NN" is a digit string representing an exponent power, and "Q" is a qualifier that indicates with the code "P" that the power is a positive decimal exponent, or the code "N" for a negative decimal exponent, or the code "B" for binary positive exponents. </p> | 0 | 1 | xsd:string | -- | |
| qudt:plainTextDescription | rdf:Property | A plain text description is used to provide a description with only simple ASCII characters for cases where LaTeX , HTML or other markup would not be appropriate. | 0 | * | -- | ||
rdf:type |
-- | 1 | * | -- | |||
@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 .