Oprava k článku „Poznámka k otázce řešitelnosti jisté soustavy nerovností kladnými čísly‟
Optimal bounds for the colored Tverberg problem
We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
Optimal control in linear systems without the condition of regular controllability
Optimal isometries for a pair of compact convex subsets of ℝⁿ
In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for metrics for all p ≥ 2 and the symmetric difference metric.
Optimal packings for filled rings of circles
General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing of circles within a circle admits a ring structure if one allows for irregular spacing of circles...
Optimal Spherical Packing of Circles and Hilbert's 14th Problem
Optimal substructures in optimal and approximate circle packings.
Optimality conditions for maximizers of the information divergence from an exponential family
The information divergence of a probability measure from an exponential family over a finite set is defined as infimum of the divergences of from subject to . All directional derivatives of the divergence from are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for to be a maximizer of the divergence from are presented, including new ones when is not projectable to .
Optimality of the Delaunay Triangulation in Rd .
Optimierung konstant belegter Ovale und ein Hyperbel-Schnittsatz
Optimisation hybride par colonies de fourmis pour le problème de découpe à deux dimensions
Nous nous intéressons dans cet article au problème de découpe guillotine en deux dimensions noté 2BP/O/G. Il s'agit de découper un certain nombre de pièces rectangulaires dans un ensemble de plaques de matière première, elles même rectangulaires et identiques. Celles-ci sont disponibles en quantité illimitée. L'objectif est de minimiser le nombre de plaques utilisées pour satisfaire la demande, en appliquant une succession de coupes, dites guillotines, allant de bout en bout. Nous proposons une approche...
Optimizing geometric measures for fixed minimal annulus and inradius.
Oriented Matroids with Few Mutations.
Orthant spanning simplexes with minimal volume.
Outer boundaries of self-similar tiles.
Outer -convex functions on a normed space.
Packing 10 or 11 unit squares in a square.
Packing and covering a unit equilateral triangle with equilateral triangles.
Packing lines, planes, etc.: Packings in Grassmannian spaces.
Packing of 180 equal circles on a sphere.