Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spac...

The idea of an oscillating Universe has remained a topic interest even after the discovery dark energy. This paper confirms this by means another well-established theory in general relativity, embedding curved spacetimes higher-dimensional flat spacetimes: n-dimensional Riemannian space is said to be class m if +n lowest dimension which given can embedded; here . So four-dimensional two and the...

We examine the action of the fundamental group Γ of an mpunctured Riemann surface on the middle dimensional homology of a regular fiber in a Lefschetz fibration, and describe to what extent this action can be recovered from the intersection numbers of vanishing cycles. Basis changes for the vanishing cycles result in a nonlinear action of the framed braid group B̃ on m strings on a suitable spac...

We address the localization of a scalar field, whose bulk-mass M is considered in a wide range including the tachyonic region, on a three-brane. The brane with non-zero cosmological constant λ is embedded in five dimensional bulk space. We find in this case that the trapped scalar could have mass m which has an upper bound and expressed as m = m20 + αM 2 ≤ β|λ| with the calculable numbers m20, ...