Related papers: Infinity modulus and the essential metric
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…
Given any closed Kaehler manifold we define, following an idea by Eugenio Calabi, a Riemannian metric on the space of Kaehler metrics regarded as an infinite dimensional manifold. We prove several geometrical features of the resulting…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy ${\mathbb {R}} P^5$ has infinitely many path components. We also show that in each dimension $4k+1$ there are at least $2^{2k}$ homotopy ${\mathbb…
In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.
In many problems of PDE involving the Laplace-Beltrami operator on manifolds with ends, it is often useful to introduce radial or geodesic normal coordinates near infinity. In this paper, we prove the existence of such coordinates for a…
We show the equivalence of several characterizations of relative hyperbolicity for metric spaces, and obtain extra information about geodesics in a relatively hyperbolic space. We apply this to characterize hyperbolically embedded subgroups…
We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta…
We describe some metric properties of incomparability graphs. We consider the problem of the existence of infinite paths, either induced or isometric, in the incomparability graph of a poset. Among other things, we show that if the…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We consider minisuperspace gravity system described by piecewise flat metric discontinuous on three-dimensional faces (tetrahedra). There are infinite terms in the Einstein action. However, starting from proper regularization, these terms…
Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild conditions suffice to imply the existence of an isomorphism…
In this paper the notion of modular cone metric space is introduced and some properties of such spaces are investigated. Also we define convex modular cone metric which takes values in CR(Y) where Y is a compact Hausdorff space. Then a…
We establish a sharp reciprocity inequality for modulus in compact metric spaces $X$ with finite Hausdorff measure. In particular, when $X$ is also homeomorphic to a planar rectangle, our result answers a question of K. Rajala and M.…
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in…