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It is now known that the complement of any polynomially convex compact set K in C^n is an Oka manifold. In particular this holds if K is convex. I will discuss a recent result, joint with Forstneri?, ...
The Hausdorff distance between a compact convex set K CRd and random sets K c lRd iS studied. Basic inequalities are derived for the case of K being a convex subset of K. If applied to special seq...
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
In this note, we give first that a characterization of super weakly compact convex sets of a Banach space X, namely, a sufficient and necessary condition for a closed bounded convex set Ksubset X to b...
Abstract: We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Anderse...
In recent studies, properties of the set of affine maps between two convex sets have been investigated with intensive motivation from quantum physics, but in those preceding works the underlying con...
In a recent paper R. Urbanski [13] investigated the mimimality of pairs compact convex sets which satisfy additional conditions, namely the minimal convex pairs. In this paper we consider some differe...
In a recent paper P. Diamond, P. Kloeden, A. Rubinov and A. Vladimirov [3] investigated comperative properties of three different metrics in the space of pairs of compact convex sets. These metrics de...
Let $K_1$ and $K_2$ be two nonempty closed convex sets in some normed space $(H,\Vert \cdot \Vert )$. This paper is concerned with the question of finding a "good" decomposition, with respect to $K_1$...
We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and o...
Every convex set in the plane gives rise to geometric functionals such as the area, perimeter, diameter, width, inradius and circumradius. In this paper, we prove new inequalities involving these geom...
This paper collects together known inequalities relating the area, perimeter, width, diameter, inradius and circumradius of planar convex sets. Also, a technique for finding new inequalities is stated...
MODELLING RANDOM CONVEX SETS          2007/8/7
A model is developed for convex-set valued data, which are the Minkowski sum of aconvex parameter set and a convex noise set. This model is generalized to include location and scale parameters. A furt...

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