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Empty convex polygons in almost convex sets
A finite set of points, in general position in the plane, is almost convex if every triple determines a triangle with at most one point in its interior. For every -; [.gt.] 3, we determine the maximum size of an almost convex
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Quasiconvex extreme points of convex sets.
If the quasiconvex hull of a compact set in $R^{mtimes n}$ is convex then also for that is in a special structure of quasiconvex extreme points of compact convex sets. In particular, weshow that compact convex<...
BA - Obecná matematika
- 2002 •
- D
Rok uplatnění
D - Stať ve sborníku
Boundedness of Convex Sets
A necessary and sufficient condition of boundedness of closed convex sets in finite dimensional linear spaces is well-known. It is proven that with a slight modification of the proof, this condition can be extended to any convex...
BA - Obecná matematika
- 2011 •
- D •
- Link
Rok uplatnění
D - Stať ve sborníku
Výsledek na webu
Weights of boundaries of compact convex sets
Let B be a boundary of a compact convex set X. We prove that the weight of X equals the weight of B provided B is Lindelof or X is a standard compact convex set and B is the set of extreme points of X....
BA - Obecná matematika
- 2010 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Finding the convex hull of a dense set
We give tight bounds on finding the convex hull of a dense set.
BD - Teorie informace
- 2007 •
- D
Rok uplatnění
D - Stať ve sborníku
Computing D-convex hulls in the plane
A real function f on R^d is called D-convex, where D is a set of vectors in R^d, if its restriction to each line parallel to a nonzero v from D is convex. The D-convex hull of a compact set A in R^d is the...
BD - Teorie informace
- 2008 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
On sets of non-differentiability of Lipschitz and convex functions
Several notes on sets of non-differentiability of Lipschitz and convex functions are presented. It is proved that the set of non-differentiability points of a convex function in a Euclidean space is sigma-strongly ...
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum
We construct a Lipschitz function on R2 which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqua...
BA - Obecná matematika
- 2014 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Holes in 2-Convex Point Sets
than l connected components. A point set S is l-convex if there exists an l-convex 2-convex point set of size n contains an Omega(log n)-hole. In comparisonLet S be a set of n points in the plane...
Pure mathematics
- 2018 •
- D •
- Link
Rok uplatnění
D - Stať ve sborníku
Výsledek na webu
Convex cores of measures on R d.
We define the convex core of a finite Borel measure Q on R d as the intersection of all convex Borel sets C with Q(C)=Q(R d). It consists exactly of means of probability measures dominated by Q. Geometric and measure-theore...
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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