Related papers: A new valuation on polyhedral cones

We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry…

We obtain some necessary and sufficient conditions for the boundedness of a family of positive operators defined on symmetric cones, we then deduce off-diagonal boundedness of associated Bergman-type operators in tube domains over symmetric…

A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.

We extend and prove a conjecture of Bengu\c{s}-Lasnier on the parametrization of valuations on a polynomial ring by certain spaces of diskoids.

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.

We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial…

We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.

An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.

In this paper we show if R is a filtered ring then we can define a quasi valuation. And if R is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for R.

We provide explicit equations and parameterizations of some new rational Gushel-Mukai fourfolds of special type.

We generalize valuations on polyhedral cones to valuations on fans. For fans induced by hyperplane arrangements, we show a correspondence between rotation-invariant valuations and deletion-restriction invariants. In particular, we define a…

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…

A classification of SL$(n)$ invariant valuations on the space of convex polytopes in $R^n$ without any continuity assumptions is established. A corresponding result is obtained on the space of convex polytopes in $R^n$ that contain the…

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

In this note we characterize isoperimetric regions inside almost-convex cones. More precisely, as in the case of convex cones, we show that isoperimetric sets are given by intersecting the cone with a ball centered at the origin.

In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.