Doust and Weston (J Funct Anal 254:2336–2364, 2008) have introduced a new method called enhanced negative type for calculating a non-trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be nontrivial. In this paper we refine the technique of enhanced negative type and ...

In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete L-fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces, intuitionistic metric spaces and L-fuzzy metric spaces.

This paper discusses the properties of Skorokhod metric on normal and upper semi-continuous fuzzy sets space. All mentioned below refer to this type sets. We confirm that enhanced-type are equivalent compact However, not necessarily L p -integrable sets, which include point out -type d metric, ≥ 1 , is well-defined in common cases but always all introduce ⁎ an expansion write as sequel. Then, w...

The L-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type M in a Riemannian manifold (N, g) induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for the geodesic distance holds also for all diffeomorphism groups for the L-metric.

The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra g without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module a in a canonical way. I...

The L-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type M in a Riemannian manifold (N, g) induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for the geodesic distance holds also for all diffeomorphism groups for the L-metric.

The increasing amount of digital audio-visual content accessible today calls for scalable solutions for content based search. The state of the art solutions reveal linear scalability in respect to the collection size due to the large number of distance computations needed for comparing low level audio-visual features. As a result, search in large audio-visual collections is limited to associate...

We introduce a notion of rank completion for bi-modules over a finite tracial von Neumann algebra. We show that the functor of rank completion is exact and that the category of complete modules is abelian with enough projective objects. This leads to interesting computations in the L 2-homology for tracial algebras. As an application, we also give a new proof of a Theorem of Gaboriau on invaria...