@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-QL0GMPR2-2
  skos:prefLabel "fonction de Rastrigin"@fr, "Rastrigin function"@en ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .

psr:-NLK2W2WF-H
  skos:prefLabel "homogeneous function"@en, "fonction homogène"@fr ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .

psr:-ZBQ8QJCZ-2
  skos:prefLabel "Rosenbrock function"@en, "fonction de Rosenbrock"@fr ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .

psr:-NWQWBV8C-X
  skos:prefLabel "transformation de Legendre"@fr, "Legendre transformation"@en ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .

psr:-M8RJGTGT-V
  skos:prefLabel "quasiconformal mapping"@en, "application quasi conforme"@fr ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .

psr: a skos:ConceptScheme .
psr:-FWTTZ9R7-X
  skos:narrower psr:-M8RJGTGT-V, psr:-QL0GMPR2-2, psr:-NXX2Z7NJ-R, psr:-NLK2W2WF-H, psr:-ZBQ8QJCZ-2, psr:-NWQWBV8C-X, psr:-Q8H0F473-5 ;
  skos:definition """In mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real values, while the "output", also called the "value of the function", may be real or complex. However, the study of the complex-valued functions may be easily reduced to the study of the real-valued functions, by considering the real and imaginary parts of the complex function. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Function_of_several_real_variables">https://en.wikipedia.org/wiki/Function_of_several_real_variables</a>)"""@en, """En mathématiques et plus spécialement en analyse vectorielle, une <b>fonction numérique à plusieurs variables</b> réelles est une fonction dont l'ensemble de départ <span class="texhtml mvar" style="font-style:italic;">E</span> est une partie du produit cartésien <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 \\\\mathbb {R} ^{n}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{n}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="\\\\mathbb {R} ^{n}"></span>. L'ensemble d'arrivée <span class="texhtml mvar" style="font-style:italic;">F</span> peut être <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 \\\\mathbb {R} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="\\\\mathbb {R} "></span> ou <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 \\\\mathbb {R} ^{p}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>p</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{p}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40a670215fd4556c78acd92bdc55d472548b7a21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.737ex; height:2.343ex;" alt="\\\\mathbb {R} ^{p}"></span>. Le second cas peut se ramener au premier cas en considérant qu'il s'agit en réalité de <span class="texhtml mvar" style="font-style:italic;">p</span> fonctions de <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 \\\\mathbb {R} ^{n}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{n}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="\\\\mathbb {R} ^{n}"></span> dans <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 \\\\mathbb {R} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="\\\\mathbb {R} "></span> appelées fonctions coordonnées.
<br/>La fonction est donc une relation associant à chaque <i>n</i>-uplet <span class="texhtml"><i>x</i> = (<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, ..., <i>x<sub>n</sub></i>)</span> élément de l'ensemble de départ un et un seul élément de l'ensemble d'arrivée, que l'on appelle image de <span class="texhtml mvar" style="font-style:italic;">x</span> par <span class="texhtml mvar" style="font-style:italic;">f</span> et que l'on note <span class="texhtml"><i>f</i>(<i>x</i>)</span> ou <span class="texhtml"><i>f</i>(<i>x</i><sub>1</sub>, ..., <i>x<sub>n</sub></i>)</span>&nbsp;:
<br/>
<br/><center><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:{\\egin{array}{ccc}E&amp;\\\\longrightarrow &amp;F\\\\\\\\(x_{1},\\\\ldots ,x_{n})&amp;\\\\longmapsto &amp;f(x_{1},\\\\ldots ,x_{n})\\\\end{array}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>f</mi>
<br/>        <mo>:</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtable columnalign="center center center" rowspacing="4pt" columnspacing="1em">
<br/>            <mtr>
<br/>              <mtd>
<br/>                <mi>E</mi>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mo stretchy="false">⟶<!-- ⟶ --></mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi>F</mi>
<br/>              </mtd>
<br/>            </mtr>
<br/>            <mtr>
<br/>              <mtd>
<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/>              </mtd>
<br/>              <mtd>
<br/>                <mo stretchy="false">⟼<!-- ⟼ --></mo>
<br/>              </mtd>
<br/>              <mtd>
<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/>              </mtd>
<br/>            </mtr>
<br/>          </mtable>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f:{\\egin{array}{ccc}E&amp;\\\\longrightarrow &amp;F\\\\\\\\(x_{1},\\\\ldots ,x_{n})&amp;\\\\longmapsto &amp;f(x_{1},\\\\ldots ,x_{n})\\\\end{array}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77ccb79a29e44247ff2704211ac36086f2a32b75" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:37.536ex; height:6.176ex;" alt="{\\\\displaystyle f:{\\egin{array}{ccc}E&amp;\\\\longrightarrow &amp;F\\\\\\\\(x_{1},\\\\ldots ,x_{n})&amp;\\\\longmapsto &amp;f(x_{1},\\\\ldots ,x_{n})\\\\end{array}}}"></span></center>
<br/>Si l'on munit les deux espaces vectoriels <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 \\\\mathbb {R} ^{n}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{n}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="\\\\mathbb {R} ^{n}"></span> et <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 \\\\mathbb {R} ^{p}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>p</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{p}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40a670215fd4556c78acd92bdc55d472548b7a21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.737ex; height:2.343ex;" alt="\\\\mathbb {R} ^{p}"></span> d'une norme, on peut étudier la continuité et la différentiabilité de telles fonctions. En fixant les <span class="texhtml mvar" style="font-style:italic;">n</span> variables réelles <span class="texhtml">(<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, ..., <i>x<sub>n</sub></i>)</span> sauf une, on se ramène à l'étude de fonctions d'une variable réelle, à valeurs dans <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 \\\\mathbb {R} ^{p}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>p</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{p}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40a670215fd4556c78acd92bdc55d472548b7a21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.737ex; height:2.343ex;" alt="\\\\mathbb {R} ^{p}"></span> (ou même dans <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 \\\\mathbb {R} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="\\\\mathbb {R} "></span>, en considérant les <span class="texhtml mvar" style="font-style:italic;">p</span> fonctions coordonnées). Leurs dérivées, lorsqu'elles existent, s'appellent les dérivées partielles de la fonction de départ. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_plusieurs_variables">https://fr.wikipedia.org/wiki/Fonction_de_plusieurs_variables</a>)"""@fr ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_de_plusieurs_variables>, <https://en.wikipedia.org/wiki/Function_of_several_real_variables> ;
  skos:altLabel "real-valued function of n real variables"@en, "real multivariate function"@en ;
  skos:prefLabel "function of several real variables"@en, "fonction numérique à plusieurs variables réelles"@fr ;
  skos:broader psr:-MDFZ99KQ-Q .

psr:-NXX2Z7NJ-R
  skos:prefLabel "Kampé de Fériet function"@en, "fonction de Kampé de Fériet"@fr ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .

psr:-MDFZ99KQ-Q
  skos:prefLabel "fonction numérique"@fr, "real-valued function"@en ;
  a skos:Concept ;
  skos:narrower psr:-FWTTZ9R7-X .

psr:-Q8H0F473-5
  skos:prefLabel "fonction de Himmelblau"@fr, "Himmelblau's function"@en ;
  a skos:Concept ;
  skos:broader psr:-FWTTZ9R7-X .