Subordination and superordination results for -like functions.
Subsets of the unit ball the are separated by more than one
Substitutions, abstract number systems and the space filling property
In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.
Successive Minima, Intrinsic Volumes, and Lattice Determinants.
Successive-Minima-Type Inequalities.
Sudakov-type minoration for log-concave vectors
We formulate and discuss a conjecture concerning lower bounds for norms of log-concave vectors, which generalizes the classical Sudakov minoration principle for Gaussian vectors. We show that the conjecture holds for some special classes of log-concave measures and some weaker forms of it are satisfied in the general case. We also present some applications based on chaining techniques.
Sufficient conditions for the extendibility of an -th order flex of polyhedra.
Suites décroissantes de simplexes
Sulla famiglia dei flocks lineari di una quadrica iperbolica assolutamente irriducibile di uno spazio proiettivo finito
In questa Nota diamo una caratterizzazione dell'insieme di tutti i flocks lineari della quadrica iperbolica assolutamente irriducibile in .
Sums of distances between points of a sphere.
Sumsets of finite Beatty sequences.
Superior estimation of Carathéodory's dimension for n-cell convexity
Supersolvable orders and inductively free arrangements
In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.
Support functions of central convex bodies
Support properties of a family of connected compact sets
A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. A special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.
Sur la classification des hexagones hyperboliques à angles droits en dimension 5
The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space , by using a quaternionic distance between geodesics in .
Sur la frontière d'un convexe mobile
Siano , sottoinsiemi convessi, chiusi e limitati di uno spazio normato , con le frontiere , . Dimostriamo che , dove è la metrica di Hausdorff tra sottoinsiemi chiusi di . Studiamo inoltre la continuità e la semicontinuità superiore ed inferiore di una multifunzione di tipo «frontiera».
Sur la rigidité de polyèdres hyperboliques en dimension : cas de volume fini, cas hyperidéal, cas fuchsien
Un polyèdre hyperbolique semi-idéal est un polyèdre dont les sommets sont dans l’espace hyperbolique ou à l’infini. Un polyèdre hyperbolique hyperidéal est, dans le modèle projectif, l’intersection de avec un polyèdre projectif dont les sommets sont tous en dehors de et dont toutes les arêtes rencontrent . Nous classifions les polyèdres semi-idéaux en fonction de leur métrique duale, d’après les résultats de Rivin dans [8] (écrit avec C.D.Hodgson) et [7]. Nous utilisons ce résultat pour retrouver...
Sur les automorphismes affines des ouverts convexes saillants
Sur les cercles tangents à trois cercles et les sphères tangentes à trois ou à quatre sphères