It is essential for insurance regulation to have a clear picture of the risk measures that are used. We compare different mathematical interpretations of the Solvency Capital Requirement (SCR) definition that can be found in the literature. We introduce a mathematical modeling framework that allows us to make a mathematically rigorous comparison. The paper shows similarities, differences, and p...

Starting from the pioneering paper of H. Blum [13], the medial axis as a descriptor and classifier of shapes and figures has been established as the best defined and studied mathematical concept in reference to thinning and skeletonization of contours and shapes [6, 7, 8, 9, 10, 11, 12, 14]. From the various mathematical tools (Maximal disks, cut loci, Voronoi sets [6, 7, 8, 9, 10, 11, 12, 13, ...

Starting from the pioneering paper of H. Blum [13], the medial axis as a descriptor and classifier of shapes and figures has been established as the best defined and studied mathematical concept in reference to thinning and skeletonization of contours and shapes [6, 7, 8, 9, 10, 11, 12, 14]. From the various mathematical tools (Maximal disks, cut loci, Voronoi sets [6, 7, 8, 9, 10, 11, 12, 13, ...

A well-clear volume is a key component of NASA’s Separation Assurance concept for the integration of UAS in the NAS. This paper proposes a mathematical definition of the well-clear volume that uses, in addition to distance thresholds, a time threshold based on time to entry point (TEP). The mathematical model that results from this definition is more conservative than other candidate definition...

The paper introduces a new approach to define process algebras with quantified transitions. A mathematical model is introduced which allows the definition of various classes of process algebras including the well known models of untimed, probabilistic and stochastic process algebras. For this general mathematical model a bisimulation equivalence is defined and it is shown that the equivalence i...

We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182 . AMS classification: 81T13, 81T75 The goal of this note is to consider gauge theories on noncommutative euclidean space and, in particular, to study the structure of gauge group. This group was an...

There are many scientific problems generated by the multiple and conflicting alternative definitions of linguistic recursion and human recursive processing that exist in the literature. The purpose of this article is to make available to the linguistic community the standard mathematical definition of recursion and to apply it to discuss linguistic recursion. As a byproduct, we obtain an insigh...

A mathematical framework for the definition of topological relationships.

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.