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We prove that the reciprocal of the volume of the polar bodies, about the Santaló point, of a shadow system of convex bodies Kt, is a convex function of t. Thus extending to the non-symmetric case a result of Campi and Gronchi. The case that the reciprocal of the volume is an affine function of t is also investigated and is characterized under certain… (More)

- Peter Puschnig, A. Daniel Boese, +8 authors F. Stefan Tautz
- The journal of physical chemistry letters
- 2017

Orbitals are invaluable in providing a model of bonding in molecules or between molecules and surfaces. Most present-day methods in computational chemistry begin by calculating the molecular orbitals of the system. To what extent have these mathematical objects analogues in the real world? To shed light on this intriguing question, we employ a photoemission… (More)

Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far a given convex body is from one with “enough symmetries”. To define these new measures of symmetry, we use affine covariant points. We give examples of convex… (More)

We answer in the negative a question by Grünbaum who asked if there exists a finite basis of affine invariant points. We give a positive answer to another question by Grünbaum about the “size” of the set of all affine invariant points. Related, we show that the set of all convex bodies K, for which the set of affine invariant points is all of R, is dense in… (More)

- Mathieu Meyer, C. El Houch, S. Barbezat
- 2016

2014 18O+ ions with energies ranging from 10 to 45 keV have been implanted along the 110 > or 100 > directions of A1, Ni and Cu single crystals. The experimental techniques used to prepare the samples and to perform the implantations are described. The implantation profiles are determined with an ion probe microanalyser. They are characteristic of… (More)

- Matthieu Fradelizi, Mathieu Meyer, Artem Zvavitch
- Discrete & Computational Geometry
- 2012

We elaborate on the use of shadow systems to prove a particular case of the conjectured lower bound of the volume product P(K) = minz∈int(K) |K|||K|, where K ⊂ R is a convex body and K = {y ∈ R : (y − z) · (x − z) 6 1 for all x ∈ K} is the polar body of K with respect to the center of polarity z. In particular, we show that if K ⊂ R is the convex hull of… (More)

- D. ROUZINEAU, Mathieu Meyer, Michèle Prévost, Xuan-Mi Meyer, J. M. RENEAUME
- 2005

based on NEQ Model D. ROUZINEAU, M. MEYER, M. PREVOST, X. MEYER, J.M. RENEAUME Laboratoire de Génie Chimique, ENSIACET 118 Route de Narbonne, 31077 Toulouse Cedex 4, France e-mail : David.Rouzineau@ensiacet.fr b Laboratoire de Thermique Energétique et Procédés, UPPA BP1155 64013 Pau, France Abstract Firstly, a non-equilibrium model (or NEQ model) has… (More)

An affine invariant point on the class of convex bodies Kn in R, endowed with the Hausdorff metric, is a continuous map from Kn to R which is invariant under one-to-one affine transformations A on R, that is, p ` A(K) ́ = A ` p(K) ́ . We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K) = p(K) for every K ∈… (More)

- J. Bonet, MI Galan, +4 authors JM Reneaume
- 2006

J Bonet, MI Galan, J Costa, R Thery, X Meyer, M Meyer, JM Reneaume Univ. de Barcelona, Dep. d’Enginyeria Quimica i Metallurgia, Marti i Franques 1, E-08028 Barcelona, Spain, E-mail: galan@angel.qui.ub.es Laboratoire de Génie Chimique, UMR-CNRS 5503, INPT-ENSIACET, 5 rue Paulin Talabot, 31106 Toulouse Cedex 01, France, E-mail: xuan.meyer@ensiacet.fr,… (More)