相关论文: The radius of metric regularity at infinity
We derive some estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part deals with general infinitely divisible distributions. The…
We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…
We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every…
Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the metric varies. Motivated by applications in topological data…
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
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.
Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…
We study quasiconformal mappings of the unit disk that have planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the inverse map, which somewhat surprisingly is almost as good as…
We prove a new Morse-Sard type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for $C^2$ mappings. We show the equivalence of three different types of regularity conditions which…
The main purpose of this note is to illustrate how the radius in a finite-dimensional power-associative algebra over a field $\mathbb{F}$, either $\mathbb{R}$ or $\mathbb{C}$, may change when the multiplication in this algebra is modified.…
In this paper we show a characterization of the joint spectral radius of a set of matrices as the limit of the $p$-radius of an associated probability distribution when $p$ tends to $\infty$. Allowing the set to have infinitely many…
A paper is devoted to study of local behavior of so-called $Q$-mappings including qua\-si\-con\-for\-mal mappings and mappings with bounded distortion. It is showed that, such mappings have removable isolated singularities whenever the grow…
In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two…
We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…
The triangular ratio metric is studied in a domain $G\subsetneq\mathbb{R}^n$, $n\geq2$. Several sharp bounds are proven for this metric, especially, in the case where the domain is the unit disk of the complex plane. The results are applied…
The covering radius of permutation group codes are studied in this paper with $l_{\infty}$-metric. We determine the covering radius of the $(p,q)$-type group, which is a direct product of two cyclic transitive groups. We also deduce the…
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in…
Regular decompositions are necessary for most superpixel-based object recognition or tracking applications. So far in the literature, the regularity or compactness of a superpixel shape is mainly measured by its circularity. In this work,…