The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

Let M denote the ideal of first category subsets of R. We prove that min{card X : X ⊆ R,X 6∈ M} is the smallest cardinality of a family S ⊆ {0, 1} with the property that for each f : ω −→ ⋃ n∈ω{0, 1} n there exists a sequence {an}n∈ω belonging to S such that for infinitely many i ∈ ω the infinite sequence {ai+n}n∈ω extends the finite sequence f(i). We inform that S ⊆ {0, 1} is not of first cate...

Let Ω ⊂ R, n ≥ 2, be a bounded domain with smooth boundary. Consider utt −4xu+ q(x, t)u = 0 in Ω× [0, T ] u(x, 0) = 0, ut(x, 0) = 0 if x ∈ Ω u(x, t) = f(x, t) on ∂Ω× [0, T ] We show that if u and f are known on ∂Ω× [0, T ], for all f ∈ C∞ 0 (∂Ω× [0, T ]), then q(x, t) may be reconstructed on C = { (x, t) : x∈Ω, 0 < t < T, x− tω & x+ (T − t)ω 6∈ Ω ∀ ω ∈ R, |ω| = 1 } provided q is known at all po...

We present a classification of m-strict limits (i.e. and |D1fk|(Ω)+|D2fk|(Ω)→|D1f|(Ω)+|D2f|(Ω)) planar BV homeomorphisms; class previously studied by the authors S. Hencl in [6]. There it was shown that such mappings allow for cavitations fractures singularities but fulfil suitable generalization INV condition. As pointed out J. Ball [3], these features are physically expected limit configurati...

BACKGROUND & AIMS Nutritional supplementation with polyunsaturated fatty acids is important in preterm infants neurodevelopment, but it is not known if the omega-6/omega-3 ratio affects this process. This study was designed to determine the effects of a balanced contribution of arachidonic acid in very preterm newborns fed with formula milk. METHODS This was a randomized trial, in which newbo...