We present an efficient algorithm that computes the Minkowski sum of two polygons, which may have holes. The new algorithm is based on the convolution approach. Its efficiency stems in part from a property for Minkowski sums of polygons with holes, which in fact holds in any dimension: Given two polygons with holes, for each input polygon we can fill up the holes that are relatively small compa...

BACKGROUND Several methodological approaches have been used to estimate distance in health service research. In this study, focusing on cardiac catheterization services, Euclidean, Manhattan, and the less widely known Minkowski distance metrics are used to estimate distances from patient residence to hospital. Distance metrics typically produce less accurate estimates than actual measurements, ...

We have investigated some issues relevant for the possibility to construct physical theories on the κ-Minkowski noncommutative spacetime. The notion of field in κ-Minkowski has been introduced by generalizing the Weyl system/map formalism and a comparative study of the star products arising from this generalization has been done. A line of analysis of the symmetries of κ-Minkowski has been prop...

We introduce and study a sequence of geometric invariants for convex bodies in finite-dimensional spaces, which is in a sense dual to the sequence of mean Minkowski measures of symmetry proposed by the second author. It turns out that the sequence introduced in this paper shares many nice properties with the sequence of mean Minkowski measures, such as the sub-arithmeticity and the upper-additi...

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study ...

We show that the response rate of ~i! a static source interacting with Hawking radiation of a massless scalar field in Schwarzschild spacetime ~with the Unruh vacuum! and that of ~ii! a uniformly accelerated source with the same proper acceleration in Minkowski spacetime ~with the Minkowski vacuum! are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle...

We show that the response rate of (i) a static source interacting with Hawking radiation of massless scalar field in Schwarzschild spacetime (with the Unruh vacuum) and that of (ii) a uniformly accelerated source with the same proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle–H...

We show that the response rate of (i) a static source interacting with Hawking radiation of massless scalar field in Schwarzschild spacetime (with the Unruh vacuum) and that of (ii) a uniformly accelerated source with the same proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle–H...

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...

In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, Cap <mm...