Skip to main content

Zonohedra, zonoids and mixtures management

  • Contributed Papers
  • Conference paper
  • First Online:
System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 197))

  • 1349 Accesses

Abstract

We presented different problems in separation theory and showed the simplicity of some geometrical solutions in the particular case we have named “regular selectivity”. Using the same geometrical framework, extensions of these solutions to some more complicated cases, will be the aim of future works.

This work was supported by Université Joseph Fourier de Grenoble (France), Centre National de la Recherche Scientifique (CNRS) and Société Nationale ELF-Aquitaine.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.D. Bolker, "A class of convex bodies", Trans. Amer. Math Soc., Vol. 145, Nov. 1969.

    Google Scholar 

  2. J. Bourgain, J. Lindenstrauss, V. Milman, "Approximation o: zonoids by zonotopes", Acta Math., 162, (1989).

    Google Scholar 

  3. H.S. Coxeter, "The classification of zonohedra by means of projective diagrams", Journ. de Math, tome XLI., Fasc. 2, 1962

    Google Scholar 

  4. H. Edelsbrunner, "Algorithms in Combinatorial Geometry", EATCS Monographs on Theoretical Computer Science, Vol. 10, Springer Verlag, 1987.

    Google Scholar 

  5. D. Girard et P. Valentin, "Zonotopes and Mixtures management", New Methods in optimization and their industrial uses", International Series of Numerical mathematics, Birkhäuser Verlag, 1988.

    Google Scholar 

  6. B. Lacolle et P. Valentin, "Les mélanges binaires: modélisation géométrique et algorithmes", Rapport de Recherche IMAG, RR. 841-M., Février 1991.

    Google Scholar 

  7. P. Mc Mullen, "On zonotopes", Trans. Amer. Math. Soc., 159 (1971), pp. 91–109.

    Article  MathSciNet  Google Scholar 

  8. N. Odeh, "Modélisation mathématique des propriétés de mélanges: B-splines et optimisation avec condition de forme", Thèse de l'Université Joseph Fourier, 19 Mars 1990.

    Google Scholar 

  9. N. Szafran, "Zonoèdres: de la géométrie algorithmique à la théorie de la séparation", Thèse de l'Université Joseph Fourier, Grenoble, Octobre 1991.

    Google Scholar 

  10. P. Valentin, "Theory of Zonoids: I A Mathematical Summary", NATO Institute of Advanced studies, Advances in Theory of Chromatography, Ferrare, Aug. 1991, F. Dondi, G. Guiochon Ed., Kluwer, 1992.

    Google Scholar 

  11. P. Valentin, "Theory of Zonoids: II Application to Chromatography", NATO Institute of Advanced studies, Advances in Theory of Chromatography, Ferrare, Aug. 1991, F. Dondi, G. Guiochon Ed., Kluwer, 1992.

    Google Scholar 

  12. W. Weyl, "Centrally symmetric bodies and distributions", Israel Jour. Math., 24 (1976), pp. 352–367.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacques Henry Jean-Pierre Yvon

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this paper

Cite this paper

Lacolle, B., Szafran, N., Valentin, P. (1994). Zonohedra, zonoids and mixtures management. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035534

Download citation

  • DOI: https://doi.org/10.1007/BFb0035534

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19893-2

  • Online ISBN: 978-3-540-39337-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics