Consider the problem of finding a point in an n-point metric space with the minimum average distance to all points. We show that this problem has no deterministic o(n 2)-query (4 − Ω(1))-approximation algorithms.

Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Φ with corresponding oriented matroid MΦ, then B (MΦ) is dual ...

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

Consider the problem of finding a point in an n-point metric space with the minimum average distance to all points. We show that this problem has no deterministic nonadaptive o(n)-query (4− Ω(1))-approximation algorithms.

In this paper several similarity measures of fuzzy soft sets are introduced. The measures are examined based on the geometric model, the set-theoretic approach and the matching function. A comparative study of these measures is done.

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We construct a geometric model for the mapping class group M(S) of a non-exceptional oriented surface S of genus g with m punctures and use it to show that the action of M(S) on the compact Hausdorff space of complete geodesic laminations for S is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of