55 citations · 565 across the 70 of their papers we have counts for
5 papers · 1 filter
Nonstandard -distances based on certain geometric constructions
Gergely Kiss, Jean-Luc Marichal
The concept of -distance was recently introduced to generalize the classical definition of distance to functions of arguments. In this paper we investigate this concept thro…
On the best constants associated with -distances
Gergely Kiss, Jean-Luc Marichal
We pursue the investigation of the concept of -distance, an -variable version of the classical concept of distance recently introduced and investigated by Kiss, Marichal, and…
A generalization of the concept of distance based on the simplex inequality
Gergely Kiss, Jean-Luc Marichal, Bruno Teheux
We introduce and discuss the concept of \emph{-distance}, a generalization to elements of the classical notion of distance obtained by replacing the triangle inequality with…
Derivative relationships between volume and surface area of compact regions in R^d
Jean-Luc Marichal, Michael Dorff
We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r = d V/A. We show that the families of regions for…
Slices, slabs, and sections of the unit hypercube
Jean-Luc Marichal, Michael J. Mossinghoff
Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimens…