Rep-tiling Euclidean space.
Residual Finiteness of Surface Groups via Tessellations.
Resultados recientes sobre mosaicos de Penrose.
Résumé de recherches sur la symétrie des polyèdres non eulériens.
Retour sur les caractères fermé et relativement ouvert du cône-barrière d'un convexe
Rhombus tilings of a hexagon with two triangles missing on the symmetry axis.
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 Energy.
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.
Rigidity of infinite disk patterns.
Rigidity of planar tilings.
Rigidity of planar tilings (Erratum).
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...
Rotation indices related to Poncelet’s closure theorem
Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.
Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...
r-zugängliche Unterdeckungen der Ebene durch kongruente Kreise. I.
r-zugängliche Unterdeckungen der Ebene durch kongruente Kreise. II.