Domain of influence

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(Tidied translations and added German and Spanish (U. Mueller))
(lang (Ja), synonyms after languages)
 
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Synonyms: Voronoi domain, Wigner-Seitz cell
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<font color="blue">Domaine d'influence</font> (''Fr''). <font color="red">Wirkungsbereich</font> (''Ge''). <font color="black">Dominio di influenza</font> (''It''). <font color="purple">影響ドメイン</font> (''Ja''). <font color="green">Dominio de influencia, celda de Wigner-Seitz</font> (''Sp'').
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'''Synonyms''': Voronoi domain, Wigner-Seitz cell
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<font color="blue">Domaine d'influence</font> (''Fr''). <font color="red">Wirkungsbereich</font> (''Ge''). <font color="black">Dominio di influenza</font> (''It''). <font color="green">Dominio de influencia, celda de Wigner-Seitz</font> (''Sp'').
 
The domain of influence of a lattice point ''P'' (Delaunay 1933), or  Dirichlet domain or Voronoi domain, consists of all points ''Q'' in space that are closer to this lattice point than to any other lattice point or at most equidistant to it, namely such that '''OP''' &#8804;|'''t''' - '''OP'''| for any vector '''t''' belonging to the vector lattice ''L''. It is the inside of the [[Wigner-Seitz cell]].  
The domain of influence of a lattice point ''P'' (Delaunay 1933), or  Dirichlet domain or Voronoi domain, consists of all points ''Q'' in space that are closer to this lattice point than to any other lattice point or at most equidistant to it, namely such that '''OP''' &#8804;|'''t''' - '''OP'''| for any vector '''t''' belonging to the vector lattice ''L''. It is the inside of the [[Wigner-Seitz cell]].  

Latest revision as of 03:48, 26 November 2018

Domaine d'influence (Fr). Wirkungsbereich (Ge). Dominio di influenza (It). 影響ドメイン (Ja). Dominio de influencia, celda de Wigner-Seitz (Sp).

Synonyms: Voronoi domain, Wigner-Seitz cell


The domain of influence of a lattice point P (Delaunay 1933), or Dirichlet domain or Voronoi domain, consists of all points Q in space that are closer to this lattice point than to any other lattice point or at most equidistant to it, namely such that OP ≤|t - OP| for any vector t belonging to the vector lattice L. It is the inside of the Wigner-Seitz cell.

See also