Random polytopes and the volume-product of symmetric convex bodies.
Random Projections of Regular Simplices.
Rapport sur la géométrie par morceaux
Realizations of regular polytopes.
Reciprocal domains and Cohen-Macaulay -complexes in .
Recognizing graph theoretic properties with polynomial ideals.
Recognizing the topology of the space of closed convex subsets of a Banach space
Redundance of vertices of the cube relatively to its minimal ellipsoid.
Regular triangles and isoclinic triangles in the Grassmann .
Rektifizierbare vierdimensionale Simplices.
Relations among rhombic, Platonic and Archimedean solids
Remarks on missing faces and generalized lower bounds on face numbers.
Remplissage de l’espace euclidien par des complexes polyédriques d’orientation imposée et de rotondité uniforme
Nous donnons une méthode de construction de complexes polyédriques dans permettant de relier entre elles des grilles dyadiques d’orientations différentes tout en s’assurant que les polyèdres utilisés ne soient pas trop plats, y compris leurs sous-faces de toutes dimensions. Pour cela, après avoir rappelé quelques définitions et propriétés simples des polyèdres euclidiens compacts et des complexes, on se dote d’un outil qui permet de remplir de polyèdres -dimensionnels un ouvert en forme de tube...
Résumé de recherches sur la symétrie des polyèdres non eulériens.
Riemann sums over polytopes
It is well-known that the -th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard rate of convergence if the sum is over the lattice, . In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.
Rigidity and flexibility of virtual polytopes
All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.
Rigidity and the Alexandrov-Fenchel Inequality.
Rigidity and the lower bound Theorem l.
Robust optimality analysis for linear programming problems with uncertain objective function coefficients: an outer approximation approach
Linear programming (LP) problems with uncertain objective function coefficients (OFCs) are treated in this paper. In such problems, the decision-maker would be interested in an optimal solution that has robustness against uncertainty. A solution optimal for all conceivable OFCs can be considered a robust optimal solution. Then we investigate an efficient method for checking whether a given non-degenerate basic feasible (NBF) solution is optimal for all OFC vectors in a specified range. When the...
Scissors congruences, I. The Gauss-Bonnet map.