Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

We examine existence and stability of relative equilibria of the nvortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero, the weak vortices tend to a circle centered on the strong vortex. A special potential function of this limiting problem can be used to characterize orbits and stabi...

Over the past few years, site-testing at the South Pole has revealed conditions that are uniquely favourable for infrared astronomy. In particular, the exceptionally low sky brightness throughout the nearand mid-infrared leads to the possibility of a modest-sized telescope achieving comparable sensitivity to that of existing 8–10 metre class telescopes. An 8 metre Antarctic telescope, if constr...

We say that a real X is n-generic relative to a perfect tree T if X is a path through T and for all Σn(T ) sets S, there exists a number k such that either X|k ∈ S or for all σ ∈ T extending X|k we have σ / ∈ S. A real X is n-generic relative to some perfect tree if there exists such a T . We first show that for every number n all but countably many reals are n-generic relative to some perfect ...

We study the linear and nonlinear stability of relative equilibria in the planar n-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological approach is taken to show that for the case of positive circulations, a relative equilibrium is linearly stable if and only if it is a nondegenerate minimum...

We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular we prove that under appropriate hypotheses there exist relative periodic orbits near relative equilibria even when th...

in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...