A new sphere packing in 20 dimensions.
A New Step in the Solution of the Szökefalvi-Nagy Problem.
A new type of orthogonality for normed planes
In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions .
A non local quantitative characterization of ellipses leading to a solvable differential relation.
A non-uniqueness theorem in the theory of Voronoi sets.
A normed space with the Beckman-Quarles property.
A note about Bezdek's conjecture on covering an annulus by strips.
A note on convex functions.
A note on convexly independent subsets of an infinite set of points.
A note on domino shuffling.
A note on equality of functional envelopes
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in , , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
A note on formal power series
In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to map into...
A Note on Geometry of Polyhedron of Three-index Transportation Problem
A note on Hayman's theorem on the bass note of a drum.
A note on how Rényi entropy can create a spectrum of probabilistic merging operators
In this paper we present a result that relates merging of closed convex sets of discrete probability functions respectively by the squared Euclidean distance and the Kullback-Leibler divergence, using an inspiration from the Rényi entropy. While selecting the probability function with the highest Shannon entropy appears to be a convincingly justified way of representing a closed convex set of probability functions, the discussion on how to represent several closed convex sets of probability functions...
A note on infinite dimensional convex sets.
A note on intersections of simplices
We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.
A note on Kakutani Lemma
A note on separation by linear mappings
A Note on Sets of Constant Width