Extensions of an elementary geometric inequality.
Extensions of an inequality of Bonnesen to D-dimensional space and curvature conditions for convex bodies.
Exterior Algebra and Projections of Polytopes.
Exterior parallelism for polyhedra.
Extremal and optimal solutions in the transshipment problem
The paper yields an investigation of the set of all finite measures on the product space with given difference of marginals. Extremal points of this set are characterized and constructed. Sets of uniqueness are studied in the relation to marginal problem. In the optimization problem the support of the optimal measure is described for a class of cost functions. In an example the optimal value is reached by an unbounded sequence of measures.
Extremal Convex Sets.
Extremal Packing and Covering Sets.
Extremal points of high-dimensional random walks and mixing times of a brownian motion on the sphere
We derive asymptotics for the probability that the origin is an extremal point of a random walk in . We show that in order for the probability to be roughly , the number of steps of the random walk should be between and for some constant . As a result, we attain a bound for the -covering time of a spherical Brownian motion.
Extremal sections of complex -balls, 0 < p ≤ 2
We study the extremal volume of central hyperplane sections of complex n-dimensional -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.
Extremal solutions of a general marginal problem
The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.
Extremaleigenschaften rotationssysmmetrischer Kegelstümpfe im gewöhnlichen Raum. (1. Teil).
Extremaleigenschaften von Kreissektoren und Halbkugeln
Extreme and exposed representing measures of the disk algebra
We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed...
Extreme points of a convex polytope and extreme rays of the corresponding convex cone
Extreme Points of Convex Sets.
Extreme positive contractions on the Hilbert space
Extreme Punkte in der Einheitskugel des Vektorraumes der trigonometrischen Prolynome.