Page 1

## Displaying 1 – 17 of 17

Showing per page

### A note on how Rényi entropy can create a spectrum of probabilistic merging operators

Kybernetika

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 Sets of Constant Width

Publications de l'Institut Mathématique

### Beleuchtungsgebiete auf dem hyperbolischen Zylinder bei geometrischer Zentralbeleuchtung aus mehreren Lichtquellen

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

### Choquetova teorie a Dirichletova úloha

Pokroky matematiky, fyziky a astronomie

### Convex universal fixers

Discussiones Mathematicae Graph Theory

In [1] Burger and Mynhardt introduced the idea of universal fixers. Let G = (V, E) be a graph with n vertices and G’ a copy of G. For a bijective function π: V(G) → V(G’), define the prism πG of G as follows: V(πG) = V(G) ∪ V(G’) and $E\left(\pi G\right)=E\left(G\right)\cup E\left({G}^{\text{'}}\right)\cup {M}_{\pi }$, where ${M}_{\pi }=u\pi \left(u\right)|u\in V\left(G\right)$. Let γ(G) be the domination number of G. If γ(πG) = γ(G) for any bijective function π, then G is called a universal fixer. In [9] it is conjectured that the only universal fixers are the edgeless graphs K̅ₙ. In this work we generalize the concept of universal...

### Herissons et multiherissons (enveloppes parametrées par leur application de Gauss)

Banach Center Publications

### Isometrien des Konvexringes

Colloquium Mathematicae

### Isometries of Spaces of Compact Convex Subsets of Metric Manifolds.

Monatshefte für Mathematik

### Many Endpoints and Few Interior Points of Geodesics.

Inventiones mathematicae

### Metric entropy of convex hulls in Hilbert spaces

Studia Mathematica

Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), $T={t}_{1},{t}_{2},...$, $||{t}_{j}||\le {a}_{j}$, by functions of the ${a}_{j}$’s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences ${\left({a}_{j}\right)}_{j=1}^{\infty }$.

### Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces

Banach Center Publications

The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.

### Moduli of rotundity and smoothness for convex bodies.

Extracta Mathematicae

### On a globalization property

Applicationes Mathematicae

Let (X,τ) be a topological space. Let Φ be a class of real-valued functions defined on X. A function ϕ ∈ Φ is called a local Φ-subgradient of a function f:X → ℝ at a point ${x}_{0}$ if there is a neighbourhood U of ${x}_{0}$ such that f(x) - f(${x}_{0}$) ≥ ϕ(x) - ϕ(${x}_{0}$) for all x ∈ U. A function ϕ ∈ Φ is called a global Φ-subgradient of f at ${x}_{0}$ if the inequality holds for all x ∈ X. The following properties of the class Φ are investigated: (a) when the existence of a local Φ-subgradient of a function f at each point implies...

### On some properties of hyperconvex spaces.

Fixed Point Theory and Applications [electronic only]

### The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...

### Zur besten Beleuchtung konvexer Polyeder

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Page 1