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Pregled bibliografske jedinice broj: 523335

Inhomogeneous extreme forms


Dutour Sikirić, Mathieu; Schuermann, Achill; Vallentin, Frank
Inhomogeneous extreme forms // Annales de l institut fourier, 62 (2012), 6; 2227-2255 doi:10.5802/aif.2748 (međunarodna recenzija, članak, znanstveni)


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Naslov
Inhomogeneous extreme forms

Autori
Dutour Sikirić, Mathieu ; Schuermann, Achill ; Vallentin, Frank

Izvornik
Annales de l institut fourier (0373-0956) 62 (2012), 6; 2227-2255

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Lattices; Delaunay polytopes; spherical t-designs; sphere packing; sphere covering; Voronoi reduction theory

Sažetak
G.F. Voronoi (1868--1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given, but a corresponding result for coverings has been missing. In this paper we bridge the two classical memoirs. By looking at the covering problem from a different perspective, we discover the missing analogue. Instead of trying to find lattices giving economical coverings we consider lattices giving, at least locally, very uneconomical ones. We classify the covering maxima up to dimension 6 and prove their existence in all dimensions beyond. New phenomena arise: Many highly symmetric lattices turn out to give uneconomical coverings ; the covering density function is not a topological Morse function. Both phenomena are in sharp contrast to the packing problem.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekti:
098-0982705-2707 - Matematičko modeliranje cirkulacije i satelitska detekcija graničnih procesa (Kuzmić, Milivoj, MZOS ) ( POIROT)

Ustanove:
Institut "Ruđer Bošković", Zagreb

Profili:

Avatar Url Mathieu Dutour Sikirić (autor)

Poveznice na cjeloviti tekst rada:

doi arxiv.org

Citiraj ovu publikaciju:

Dutour Sikirić, Mathieu; Schuermann, Achill; Vallentin, Frank
Inhomogeneous extreme forms // Annales de l institut fourier, 62 (2012), 6; 2227-2255 doi:10.5802/aif.2748 (međunarodna recenzija, članak, znanstveni)
Dutour Sikirić, M., Schuermann, A. & Vallentin, F. (2012) Inhomogeneous extreme forms. Annales de l institut fourier, 62 (6), 2227-2255 doi:10.5802/aif.2748.
@article{article, author = {Dutour Sikiri\'{c}, Mathieu and Schuermann, Achill and Vallentin, Frank}, year = {2012}, pages = {2227-2255}, DOI = {10.5802/aif.2748}, keywords = {Lattices, Delaunay polytopes, spherical t-designs, sphere packing, sphere covering, Voronoi reduction theory}, journal = {Annales de l institut fourier}, doi = {10.5802/aif.2748}, volume = {62}, number = {6}, issn = {0373-0956}, title = {Inhomogeneous extreme forms}, keyword = {Lattices, Delaunay polytopes, spherical t-designs, sphere packing, sphere covering, Voronoi reduction theory} }
@article{article, author = {Dutour Sikiri\'{c}, Mathieu and Schuermann, Achill and Vallentin, Frank}, year = {2012}, pages = {2227-2255}, DOI = {10.5802/aif.2748}, keywords = {Lattices, Delaunay polytopes, spherical t-designs, sphere packing, sphere covering, Voronoi reduction theory}, journal = {Annales de l institut fourier}, doi = {10.5802/aif.2748}, volume = {62}, number = {6}, issn = {0373-0956}, title = {Inhomogeneous extreme forms}, keyword = {Lattices, Delaunay polytopes, spherical t-designs, sphere packing, sphere covering, Voronoi reduction theory} }

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka::


  • MathSciNet


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