arXiv subjects

Peter A. Hasto

Publications and source records attributed to Peter A. Hasto.

5 recordsLinked to original sources

arXiv2002

A New Weighted Metric: the Relative Metric I

The M-relative distance, denoted by ρ_M is a generalization of the p-relative distance, which was introduced by Ren-Cang Li. We establish necessary and sufficient conditions under which ρ_M is a metric. In two special cases we derive complete characterizations of the metric. We also present a way of extending the results to metrics sensitive to the domain in which they are defined, thus finding some connections to previously studied metrics. An auxiliary result of independent interest is an inequality related to Pittenger's inequality in Section 4.

math.MG↗

arXiv2002

Inequalities of relative weighted metrics

In this paper we present inequalities between two generalizations of the hyperbolic metric and the j_G metric. We also prove inequalities between generalized versions of the j_G metric and Seittenranta's metric.

math.MG↗

arXiv2001

A New Weighted Metric: the Relative Metric II

In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generalizations of the hyperbolic metric.

math.MG↗

arXiv2001

Distortion in the Spherical Metric under Quasiconformal Mappings

This paper contains bounds for the distortion in the spherical metric, that is to say bounds for the constant of Holder continuity of mappings f : (\Rn,q) -> (\Rn, q) where q denotes the spherical metric. The mappings considered are K-quasiconformal (K >= 1) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as K -> 1.

math.CA↗

arXiv2000

On Descents in Standard Young Tableaux

In this paper, explicit formulae for the expectation and the variance of descent functions on random standard Young tableaux are presented. Using these, it is shown that the normalized variance, $V/E^2$, is bounded if and only if a certain inequality relating tableau shape to the descent function holds.

math.CO↗