Separation in the polytope algebra.
Separation of convex polyhedral sets with column parameters
Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the...
Separation of -families of sets in general position in
In this paper the main result in [1], concerning -families of sets in general position in , is generalized. Finally we prove the following theorem: If is a family of compact convexly connected sets in general position in , then for each proper subset of the set of hyperplanes separating and is homeomorphic to .
Separation of two convex sets by operators
Séries de croissance et polynômes d'Ehrhart associés aux réseaux de racines
Étant donnés un système de racines d’une des familles A, B, C, D, F, G et le groupe abélien libre qu’il engendre, on calcule explicitement la série de croissance de ce groupe relativement à Les résultats s’interprètent en termes du polynôme d’Ehrhart de l’enveloppe convexe de .
Sets Expressible as Unions of Staircase -Convex Polygons
Let and be fixed, , , and let be a simply connected orthogonal polygon in the plane. For lies in a staircase -convex orthogonal polygon in if and only if every two points of see each other via staircase -paths in . This leads to a characterization for those sets expressible as a union of staircase -convex polygons , .
Sets invariant under projections onto one dimensional subspaces
The Hahn–Banach theorem implies that if is a one dimensional subspace of a t.v.s. , and is a circled convex body in , there is a continuous linear projection onto with . We determine the sets which have the property of being invariant under projections onto lines through subject to a weak boundedness type requirement.
Sets invariant under projections onto two dimensional subspaces
The Blaschke–Kakutani result characterizes inner product spaces , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace there is a norm 1 linear projection onto . In this paper, we determine which closed neighborhoods of zero in a real locally convex space of dimension at least 3 have the property that for every 2 dimensional subspace there is a continuous linear projection onto with .
Sets of constant width and diametrically complete setes in normed spaces
Sets with large Borsuk number.
Shaking compact sets.
Shape tiling.
Sharpening on Mircea's inequality.
Shellability of a poset of polygonal subdivisions.
Shellable Decompositions of Cells and Spheres.
Shelling Pseudopolyhedra.
Shift inequalities of Gaussian type and norms of barycentres
We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.
Shortest Watchman Routes in Simple Polygons.
Shortness coefficient of cyclically 5-connected cubic planar graphs.
Shortness coefficient of cyclically 5-connected cubic planar graphs. (Short Communication).