Recent galaxy redshift surveys have brought in a large amount of accurate cosmological data out to redshift 0.3, and future surveys are expected to achieve a high degree of completeness out to a redshift exceeding 1. Consequently, a numerical programme for determining the metric of the universe from observational data will soon become practical; and thereby realise the ultimate application of E...

In this paper, generalized metrics mean taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every metric space, if set of Archimedean equivalence classes range group has an infinite decreasing sequence, then non-empty closed subset space is a uniform retract ambient space. Next construct simultaneous extensions and ultrametrics. From existenc...

in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

and Applied Analysis 3 The condition of right K-completeness for X, p leaves outside the scope of this theorem an important class of asymmetric normed spaces, the asymmetric normed spaces associated to normed lattices because these spaces are right K-complete only for the trivial case 13 . In this paper, we give a uniform boundedness type theorem in the setting of asymmetric normed spaces which...

The complexity (quasi-metric) space has been introduced as a part of the development of a topological foundation for the complexity analysis of algorithms ([12]). Applications of this theory to the complexity analysis of Divide & Conquer algorithms have been discussed in [12]. Here we obtain several quasi-metric properties of the complexity space. The main results obtained are the Smyth-complet...

In this paper, we prove a common fixed point theorem for hybrid pairs of set and single valued mappings without assuming compatibility and continuity of any mapping on noncomplete metric spaces. To prove the theorem, we use a noncompatible condition, that is, weak commutativity of type (KB). We show that completeness of the whole space is not necessary for the existence of common fixed point. O...

Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixedinteger optimization approaches to find optimal distance metrics that generalize the Mahalanobis metric extensively studied in the literature. Additionally, we generalize and improve upon leading methods by removing reliance on pre-designated “target neighbo...