Related papers: On angular measures in axiomatic Euclidean planar …
Classical integral geometry takes place in Euclidean space, but one can attempt to imitate it in any other metric space. In particular, one can attempt this in R^n equipped with the metric derived from the p-norm. This has, in effect, been…
Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidean space enhanced with a radial probability measure. A…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We define new geometric constants for normed planes, determine their optimal values, and characterize types of planes for which these optimal values are attained. Relations of these constants to several topics, such as areas and distances…
This paper is a sequel to arXiv:2511.01024 (Base 1), where an axiomatic framework for angles and the foundations of difference-angle geometry were introduced. In difference-angle geometry, where the difference of slopes of lines is treated…
In this paper, we overlay a continuum of analytical relations which essentially serve to compute the arc-length described by a celestial body in an elliptic orbit within a stipulated time interval. The formalism is based upon a…
The main result of this article is a geometric interpretation of magnitude, a real-valued invariant of metric spaces. We introduce a Euclidean embedding of a (suitable) finite metric space $X$ such that the magnitude of $X$ can be expressed…
Chenciner and Jimenez Perez showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general Euclidean space form a convex polytope. In this note we explain how this result…
The main goal of this work is to introduce an analogous in the non-archimedean context of the Gelfand spaces of certain Banach commutative algebras with unit. In order to do that, we study the spectrum of this algebras and we show that,…
Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this…
In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…
We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call epsilon-measures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in non-Archimedean…
We construct a planar homogeneous self-similar measure, with strong separation, dense rotations and dimension greater than $1$, such that there exist lines for which dimension conservation does not hold and the projection of the measure is…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…
Integer geometry on a plane deals with objects whose vertices are points in $\mathbb Z^2$. The congruence relation is provided by all affine transformations preserving the lattice $\mathbb Z^2$. In this paper we study circumscribed circles…
Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…