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 ...

In recent years many deterministic parabolic equations have been shown to possess global attractors which, despite being subsets of an infinite-dimensional phase space, are finite-dimensional objects. Debussche showed how to generalize the deterministic theory to show that the random attractors of the corresponding stochastic equations have finite Hausdorff dimension. However, to deduce a param...

Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching point set surfaces, which is invariant with respect to isometries. A set of reference points, evenly distributed on the point set surface, is sampled by farthest point samp...