qudt:QuantityKindDimensionVector

URI: http://qudt.org/schema/qudt/QuantityKindDimensionVector

Type
Description

A 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.

Properties
qudt:informativeReference
http://en.wikipedia.org/wiki/Dimensional_analysis
http://web.mit.edu/2.25/www/pdf/DA_unified.pdf
sh:property
rdfs:subClassOf 
`dimension exponent for amount of substance` exactly 1
`dimension exponent for electric current` exactly 1
`dimension exponent for length` exactly 1
`dimension exponent for luminous intensity` exactly 1
`dimension exponent for mass` exactly 1
`dimension exponent for thermodynamic temperature` exactly 1
`dimension exponent for time` exactly 1
`dimensionless exponent` exactly 1
`latex definition` max 1
rdf:type
Annotations
rdfs:comment

A 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.

rdfs:isDefinedBy
rdfs:label
Quantity Kind Dimension Vector
View as:  CSV

Work in progress

RDF/XML 
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    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
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    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForThermodynamicTemperature"/>
    <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Class"/>
    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForElectricCurrent"/>
    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-latexDefinition"/>
    <j.0:informativeReference rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://web.mit.edu/2.25/www/pdf/DA_unified.pdf</j.0:informativeReference>
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    <rdfs:label>Quantity Kind Dimension Vector</rdfs:label>
    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForMass"/>
    <rdf:type rdf:resource="http://www.w3.org/2000/01/rdf-schema#Class"/>
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    <rdfs:subClassOf rdf:nodeID="A4"/>
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    <rdfs:subClassOf rdf:nodeID="A5"/>
    <rdfs:subClassOf rdf:nodeID="A6"/>
    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForLuminousIntensity"/>
    <rdfs:subClassOf rdf:nodeID="A7"/>
    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionlessExponent"/>
    <rdfs:subClassOf rdf:nodeID="A8"/>
    <rdfs:comment rdf:datatype="http://www.w3.org/1999/02/22-rdf-syntax-ns#HTML">&lt;p class="lm-para"&gt;A  &lt;em&gt;Quantity Kind Dimension Vector&lt;/em&gt; 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 \(dim \, Q = L^{\alpha} \, M^{\beta} \, T^{\gamma} \, I ^{\delta} \, \theta ^{\epsilon} \, N^{\eta} \, J ^{\nu}\).&lt;/p&gt;

&lt;p class="lm-para"&gt;The rational powers of the dimensional exponents, \(\alpha, \, \beta, \, \gamma, \, \delta, \, \epsilon, \, \eta, \, \nu\), are positive, negative, or zero.&lt;/p&gt;

&lt;p class="lm-para"&gt;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.&lt;/p&gt;</rdfs:comment>
    <j.1:property rdf:resource="http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForLength"/>
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TURTLE 
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<http://qudt.org/schema/qudt/QuantityKindDimensionVector>
  rdf:type rdfs:Class ;
  rdf:type owl:Class ;
  rdf:type <http://www.w3.org/ns/shacl#NodeShape> ;
  <http://qudt.org/schema/qudt/informativeReference> "http://en.wikipedia.org/wiki/Dimensional_analysis"^^xsd:anyURI ;
  <http://qudt.org/schema/qudt/informativeReference> "http://web.mit.edu/2.25/www/pdf/DA_unified.pdf"^^xsd:anyURI ;
  rdfs:comment """<p class=\"lm-para\">A  <em>Quantity Kind Dimension Vector</em> 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}\\).</p>

<p class=\"lm-para\">The rational powers of the dimensional exponents, \\(\\alpha, \\, \\beta, \\, \\gamma, \\, \\delta, \\, \\epsilon, \\, \\eta, \\, \\nu\\), are positive, negative, or zero.</p>

<p class=\"lm-para\">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.</p>"""^^rdf:HTML ;
  rdfs:isDefinedBy <http://qudt.org/2.1/schema/qudt> ;
  rdfs:isDefinedBy <http://qudt.org/2.1/schema/shacl/qudt> ;
  rdfs:label "Quantity Kind Dimension Vector" ;
  rdfs:subClassOf <http://qudt.org/schema/qudt/Concept> ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  rdfs:subClassOf [] ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForAmountOfSubstance> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForElectricCurrent> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForLength> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForLuminousIntensity> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForMass> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForThermodynamicTemperature> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionExponentForTime> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-dimensionlessExponent> ;
  <http://www.w3.org/ns/shacl#property> <http://qudt.org/schema/qudt/QuantityKindDimensionVector-latexDefinition> ;
.
JSON 
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 ,"properties":["comment":"&lt;p class=\"lm-para\"&gt;A  &lt;em&gt;Quantity Kind Dimension Vector&lt;\/em&gt; 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}\\).&lt;\/p&gt;\n\n&lt;p class=\"lm-para\"&gt;The rational powers of the dimensional exponents, \\(\\alpha, \\, \\beta, \\, \\gamma, \\, \\delta, \\, \\epsilon, \\, \\eta, \\, \\nu\\), are positive, negative, or zero.&lt;\/p&gt;\n\n&lt;p class=\"lm-para\"&gt;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.&lt;\/p&gt;" 
    ,"informative reference":"http:\/\/en.wikipedia.org\/wiki\/Dimensional_analysis" 
    ,"informative reference":"http:\/\/web.mit.edu\/2.25\/www\/pdf\/DA_unified.pdf" 
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    ,"isDefinedBy":"&lt;http:\/\/qudt.org\/2.1\/schema\/shacl\/qudt&gt;" 
    ,"label":"Quantity Kind Dimension Vector" 
    ,"property":"qudt:QuantityKindDimensionVector-dimensionExponentForAmountOfSubstance" 
    ,"property":"qudt:QuantityKindDimensionVector-dimensionExponentForElectricCurrent" 
    ,"property":"qudt:QuantityKindDimensionVector-dimensionExponentForLength" 
    ,"property":"qudt:QuantityKindDimensionVector-dimensionExponentForLuminousIntensity" 
    ,"property":"qudt:QuantityKindDimensionVector-dimensionExponentForMass" 
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JSON-LD 
{
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  "informativeReference" : [ "http://en.wikipedia.org/wiki/Dimensional_analysis", "http://web.mit.edu/2.25/www/pdf/DA_unified.pdf" ],
  "comment" : "<p class=\"lm-para\">A  <em>Quantity Kind Dimension Vector</em> 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}\\).</p>\n\n<p class=\"lm-para\">The rational powers of the dimensional exponents, \\(\\alpha, \\, \\beta, \\, \\gamma, \\, \\delta, \\, \\epsilon, \\, \\eta, \\, \\nu\\), are positive, negative, or zero.</p>\n\n<p class=\"lm-para\">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.</p>",
  "isDefinedBy" : [ "http://qudt.org/2.1/schema/shacl/qudt", "http://qudt.org/2.1/schema/qudt" ],
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