The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners PU89, PS89] and to low-distortion embeddings in low-dimensional spaces LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio fo...

The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners PU89, PS89, ADDJS90, CDNS92] and to low-distortion embeddings in low-dimensional spaces LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized per...

Our previous work in computer-aided mammography has used scale orientation pixel signatures to provide a rich description of local structure. However, when treated as vectors for statistical classi cation, the Euclidean space they de ne has unsatisfactory metric properties. In this paper we describe a scheme that makes use of a previously described signature similarity measure to de ne a non-li...

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any spinor. Suitable integral formulas allow us to prove similar properties in case of a compact Riemannian manifold equipped with a metric connection of skew-sy...

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.

a common fixed point result for weakly increasing mappings satisfying generalized contractive type of zhang in ordered metric spaces are derived.

in this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy m-complete metric spaces. we also give an affirmative partial answer to a question posed by wardowski [d. wardowski, fuzzy contractive mappings and fixed points in fuzzy metric spaces, fuzzy set syst., {bf 222}(2013), 108-114].some examples are also g...

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

Resolving the incompleteness of Weil-Petersson metric on Teichmüller spaces by taking metric and geodesic completion results in two distinct spaces, where the Hopf-Rinow theorem is no longer relevant due to the singular behavior of the Weil-Petersson metric. We construct a geodesic completion of the Teichmüller space through the formalism of Coxeter complex with the Teichmüller space as its non...