Abstract We establish a relationship between asymptotic regularity and common stationary points of multivalued mappings on metric space. As consequence our results, we obtain new fixed point result for two asymptotically regular single-valued mappings. Our work significantly improves complements comparable results in the literature.

I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

In this note, we prove that the family of regular codes is not asymptotically good. The notation follows that in [2]. All codes considered are binary linear codes. H7 refers to the [7, 4] binary Hamming code. Definition 1. A binary linear code is regular iff it does not contain as a minor any code equivalent to H7 or H 7 . It follows from the theorem that the family of regular codes, which we w...

Let T be a tree with t vertices. Clearly, an n vertex graph contains at most n/t vertex disjoint trees isomorphic to T . In this paper we show that for every > 0, there exists a D( , t) > 0 such that, if d > D( , t) and G is a simple d-regular graph on n vertices, then G contains at least (1− )n/t vertex disjoint trees isomorphic to T .