Related papers: A new valuation on polyhedral cones
We introduce a new family of orthogonal polynomials on the disk that has emerged in the context of wave propagation in layered media. Unlike known examples, the polynomials are orthogonal with respect to a measure all of whose even moments…
We characterize the valuations on the space of quasi-concave functions defined on the $N$-dimensional Euclidean space, that are rigid motion invariant and continuous with respect to a suitable topology. Among them we also provide a specific…
This article presents a new way to classify geodesics on a cone in the Euclidean 3-space. This proof is obtained considering our main result, which establishes the necessary and sufficient conditions that a curve in space must satisfy: to…
We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine, under a mild assumption on the distribution, the…
Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
We define a new class of integrable vertex models associated to quantum groups at roots of unit
We define a new class of orthogonal polyhedra, called orthogrids, that can be unfolded without overlap with constant refinement of the gridded surface.
This article is the third part of the series of articles where the theory of valuations on manifolds is constructed. In math.MG/0503399 the notion of a smooth valuation on a manifold was introduced. The goal of this article is to put a…
We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…
On objects of a triangulated category with a stability condition, we construct a topology.
It is shown that every continuous valuation defined on the $n$-dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly…
In this article we introduce a family of valuative invariants defined in terms of the $p$-th moment of the expected vanishing order. These invariants lie between $\alpha$ and $\delta$-invariants. They vary continuously in the big cone and…
We introduce the notion of a bounded weight function on a language, and show that the set of bounded weight functions on a regular language is a rational polyhedral cone. We study the cell recognised by a bounded weight function (that is,…
We study three families of polyhedral cones whose sections are regular simplices, cubes, and crosspolytopes. We compute solid angles and conic intrinsic volumes of these cones. We show that several quantities appearing in stochastic…
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
Classifications of $\rm{SL}(n)$ covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, are introduced and our classifications give unified…
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
In this paper we provide a large new family of embedded capillary surfaces inside polyhedral regions in the Euclidean space. The angle of contact of the examples we furnish is prescribed to be any value in $(\frac{\pi}{2}, \pi]$ and it is…