In contrast to SPD matrices, few tools exist perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built as quotient affine-invariant by congruence action positive diagonal space matrices had always been thought a homogeneous space. contrast, we view in this work Lie group and left-invariant metric. This unexpected new vie...

inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...

We study the positive Hermitian curvature flow on space of left-invariant metrics complex Lie groups. show that in nilpotent case, exists for all times and subconverges Cheeger-Gromov sense to a soliton. also convergence soliton when group is almost abelian. That is, its algebra admits (complex) co-dimension one abelian ideal. Finally, we solitons almost-abelian setting. prove uniqueness comple...

An invariant mean on a group G is a normalized, positive, translation invariant linear functional defined on the space of all bounded complex valued functions on G. Some groups possess an invariant mean (or are said to be amenable), while others do not. In particular, all abelian groups are amenable [2, §17.5]. An invariant mean on a group need not be inversion invariant. It is quite easy to sh...

using a generalized spherical mean operator, we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the (&apos;; p)-dunkl lipschitz condition in the space lp(rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

In this paper we study homogeneous geodesics in a three-dimensional connected Lie group G equipped with a left invariant Randers metric and investigates the set of all homogeneous geodesics. We show that there is a three-dimensional unimodular Lie group with a left invariant non-Berwaldian Randers metric which admits exactly one homogeneous geodesic through the identity element. Mathematics Sub...

This paper is a review of recent results on integrable nonholonomic geodesic flows of left–invariant metrics and leftand right–invariant constraint distributions on compact Lie groups.