The dominated hypervolume (or S-metric) is a commonly accepted quality measure for comparing approximations of Pareto fronts generated by multi-objective optimizers. Since optimizers exist, namely evolutionary algorithms, that use the S-metric internally several times per iteration, a fast determination of the S-metric value is of essential importance. This work describes how to consider the S-...

Let (W,d) be a metric space and S = {s1 . . . sk} an ordered list of subsets of W . The distance between p ∈ W and si ∈ S is d(p, si) = min{ d(p, q) : q ∈ si }. S is a resolving set forW if d(x, si) = d(y, si) for all si implies x = y. A metric basis is a resolving set of minimal cardinality, named the metric dimension of (W,d). The metric dimension has been extensively studied in the literatur...

This probably doesn’t deserve a § all to itself, but it will be handy to know it in what follows. Recall that a set S in a metric (or topological) space X is dense-in-itself 1 if every neighborhood of each s0 ∈ S contains points s ∈ S different from s0. One says that S is perfect if it is closed and dense-in-itself. A topological (or metric) space is separable if it has a countable subset whose...

We consider the space of all quasifuchsian metrics on the product of a surface with the real line. We show that, in a neighborhood of the submanifold consisting of fuchsian metrics, every non-fuchsian metric is completely determined by the bending data of its convex core. Let S be a surface of finite topological type, obtained by removing finitely many points from a compact surface without boun...

As important examples in the superstring theory and non-Kähler complex geometry, the complex manifolds #k(S 3×S3) for any k ≥ 2 [4, 11] also admit a non-vanishing holomorphic three-form [4] and a balanced metric [5]. Moreover, we know that #k(S 3 × S3) satisfies the ∂∂̄–lemma [4]. A natural question to ask is, whether #k(S 3 ×S3) admit a balanced metric ω0 such that (1.2) holds. Such a metric ω0...

In this paper, we obtain a characterization of linear spaces which may be normed so as to become complete, linear, normed metric spaces. In this connection, K. Kunugui and M. Fréchet have shown that every metric space S is isometric with a subset of a complete, linear, normed metric space. I t follows from our result that if the cardinal number of 5 is the limit of a denumerable sequence of car...

‎In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath  might be called their  definitive versions. Also, we show that there are examples which show that our main theorems are  genuine generalizations of Theorem 3.1 and 3.2 of [M.A. Miandaragh, M. Postolache and S. Rezapour,  {it Approximate fixed points of generalized convex contractions}, Fixed Poi...

The purpose of this research is to propose an effective color metric which can predict the perceptual image quality for Retinex method. In this paper, we first give a brief introduction of three kinds of typical single Retinex methods to improve the color reproduction. And then, we state the process for obtaining the observer rating value from the subjective evaluation experiment performed unde...