相关论文: Spaces of extremal magnitude

The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…

A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some…

There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of…

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

We prove necessary and sufficient integral conditions involving extremal distance for a conformal mapping of the unit disk to belong to the Hardy or weighted Bergman spaces. We also give characterizations for the Hardy number and the…

Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…

The great emptiness is a possible beginning of the Universe in the infinite past of physical time. For the epoch of great emptiness particles are extremely rare and effectively massless. Only expectation values of fields and average…

Let (X,d) be a metric space of p-negative type. Recently I. Doust and A. Weston introduced a quantification of the p-negative type property, the so called gap {\Gamma} of X. This talk introduces some formulas for the gap {\Gamma} of a…

Magnitude homology was introduced by Hepworth and Willerton in the case of graphs, and was later extended by Leinster and Shulman to metric spaces and enriched categories. Here we introduce the dual theory, magnitude cohomology, which we…

Let (\Omega,\mu) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L^p(\mu;X) is relatively compact if and only if it is…

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an…

First principles do imply a non-zero minimal distance between events in spacetime, but no positive lower bound to the precision of the measurement of a single coordinate.

Hepworth, Willerton, Leinster and Shulman introduced the magnitude homology groups for enriched categories, in particular, for metric spaces. The purpose of this paper is to describe the magnitude homology group of a metric space in terms…

This contribution is a technical description of details for implementing infinite elements. The novelty is the closed, analytic form used for most quantities.

We find necessary and sufficient conditions under which an arbitrary metric space $X$ has a unique pretangent space at the marked point $a\in X$. Key words: Metric spaces; Tangent spaces to metric spaces; Uniqueness of tangent metric…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

A left order on a magma (e.g., semigroup) is a total order of its elements that is left invariant under the magma operation. A natural topology can be introduced on the set of all left orders of an arbitrary magma. We prove that this…

"Spatial" or "geometric" quantiles are the only multivariate quantiles coping with both high-dimensional data and functional data, also in the framework of multiple-output quantile regression. This work studies spatial quantiles in the…

This paper develops an infinitesimal order of magnitude coupled with overflow technique that allows nonnumerical proofs of nondegenerate and degenerate inverse mapping theorems for mappings minimally regular at a point. This approach is…

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…