in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

This chapter presents a method for vote-based 3D shape recognition and registration, in particular using mean shift on 3D pose votes in the space of direct similarity transformations for the first time. We introduce a new distance between poses in this space—the SRT distance. It is left-invariant, unlike Euclidean distance, and has a unique, closed-form mean, in contrast to Riemannian distance,...

Abstract We establish general “collapse to the mean” principles that provide conditions under which a law-invariant functional reduces an expectation. In convex setting, we retrieve and sharpen known results from literature. However, our also apply beyond setting. illustrate this by providing complete account of for quasiconvex functionals. special cases consistent risk measures Choquet integra...

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamilton...

We provide techniques for studying the nonnegatively curved leftinvariant metrics on a compact Lie group. For “straight” paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity property of the initial derivative of curvature. We apply this result to obtain a partial classification of the nonnegatively curved left-inv...