@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-FWTTZ9R7-X
  skos:prefLabel "fonction numérique à plusieurs variables réelles"@fr, "function of several real variables"@en ;
  a skos:Concept ;
  skos:narrower psr:-NLK2W2WF-H .

psr: a skos:ConceptScheme .
psr:-RRBN6FVB-9
  skos:prefLabel "opérateur différentiel"@fr, "differential operator"@en ;
  a skos:Concept ;
  skos:narrower psr:-NLK2W2WF-H .

psr:-NLK2W2WF-H
  skos:broader psr:-RRBN6FVB-9, psr:-FWTTZ9R7-X ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_homog%C3%A8ne>, <https://en.wikipedia.org/wiki/Homogeneous_function> ;
  skos:prefLabel "fonction homogène"@fr, "homogeneous function"@en ;
  skos:definition """En mathématiques, une fonction homogène est une fonction qui a un comportement d’échelle multiplicatif par rapport à son ou ses arguments : si l'argument (vectoriel au besoin) est multiplié par un scalaire, alors le résultat sera multiplié par ce scalaire porté à une certaine puissance. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_homog%C3%A8ne">https://fr.wikipedia.org/wiki/Fonction_homog%C3%A8ne</a>)"""@fr, """In mathematics, a <b>homogeneous function</b> is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the <b>degree of homogeneity</b>, or simply the <i>degree</i>; that is, if <span class="texhtml mvar" style="font-style:italic;">k</span> is an integer, a function <span class="texhtml mvar" style="font-style:italic;">f</span> of <span class="texhtml mvar" style="font-style:italic;">n</span> variables is homogeneous of degree <span class="texhtml mvar" style="font-style:italic;">k</span> if
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle f(sx_{1},\\\\ldots ,sx_{n})=s^{k}f(x_{1},\\\\ldots ,x_{n})}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>f</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>s</mi>
<br/>        <msub>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <mi>s</mi>
<br/>        <msub>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <msup>
<br/>          <mi>s</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>k</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mi>f</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <msub>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f(sx_{1},\\\\ldots ,sx_{n})=s^{k}f(x_{1},\\\\ldots ,x_{n})}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be45f64ccf198bc94e7251807b019ba6fae02571" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:33.855ex; height:3.176ex;" alt="{\\\\displaystyle f(sx_{1},\\\\ldots ,sx_{n})=s^{k}f(x_{1},\\\\ldots ,x_{n})}"></span></dd></dl>
<br/>for every <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle x_{1},\\\\ldots ,x_{n},}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle x_{1},\\\\ldots ,x_{n},}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fb4ea72660b223c376e371c2301215a39e53a55" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:10.757ex; height:2.009ex;" alt="x_{1},\\\\ldots ,x_{n},"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle s\\
eq 0.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>s</mi>
<br/>        <mo>≠<!-- ≠ --></mo>
<br/>        <mn>0.</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle s\\
eq 0.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/325558648e6f31f7d1050afead1d4d289f3936d7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:5.998ex; height:2.676ex;" alt="{\\\\displaystyle s\\
eq 0.}"></span> 
<br/>For example, a homogeneous polynomial of degree <span class="texhtml mvar" style="font-style:italic;">k</span> defines a homogeneous function of degree <span class="texhtml mvar" style="font-style:italic;">k</span>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Homogeneous_function">https://en.wikipedia.org/wiki/Homogeneous_function</a>)"""@en ;
  dc:created "2023-08-21"^^xsd:date ;
  dc:modified "2023-08-21"^^xsd:date ;
  skos:inScheme psr: ;
  a skos:Concept .