Motivated by a scheduling problem that arises in the study of optical networks we prove the following result, which is a variation of a conjecture of Haxell, Wilfong and Winkler. Let k, n be two integers, let wsj , 1 ≤ s ≤ n, 1 ≤ j ≤ k be non-negative reals satisfying ∑k j=1 wsj < 1/n for every 1 ≤ s ≤ n and let dsj be arbitrary non-negative reals. Then there are real numbers x1, x2, . . . , xn...

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pseudo Uryshon) - fs bicsp's introduced both their induced bitopological spaces. It shown that hereditary property satisfied for with respect to but other mentioned types separations satisfies clos...

Let S be a surface of finite type which is not a sphere with at most four punctures, a torus with at most two punctures, or a closed surface of genus two. Let MF be the space of equivalence classes of measured foliations of compact support on S and let UMF be the quotient space of MF obtained by identifying two equivalence classes whenever they can be represented by topologically equivalent fol...

Consider a set of simple closed curves on a surface of genus g which fill the surface and which pairwise intersect at most once. We show that the asymptotic growth rate of the smallest number in such a set is 2 √ g as g → ∞. More generally, we give a precise asymptotic for filling sets of curves which pairwise intersect at most K ≥ 1 times. We then bound from below the cardinality of a filling ...

From a pseudo-triangulation with n tetrahedra T of an arbitrary closed orientable connected 3-manifold (for short, a 3D-space) M, we present a gem J , inducing S, with the following characteristics: (a) its number of vertices is O(n); (b) it has a set of p pairwise disjoint couples of vertices {ui, vi}, each named a twistor; (c) in the dual (J ) of J ′ a twistor becomes a pair of tetrahedra wit...