We consider the equation (1) ε∆u = (u− a(x))(u − 1) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R, ν the outer unit normal to ∂Ω, and a a smooth function satisfying −1 < a(x) < 1 in Ω. We set K, Ω+ and Ω− to be respectively the zero-level set of a, {a > 0} and {a < 0}. Assuming ∇a 6= 0 on K and a 6= 0 on ∂Ω, we show that there exists a sequence εj → 0 such that equation (1)...

Objective(s): Occludin is essential for proper assembly of tight junctions (TJs) which regulate paracellular endothelial permeability. Omega-3 polyunsaturated fatty acids (Ω-3 PUFA) protect endothelial barrier function against injury. Materials and Methods: We examined anti-inflammatory effect of Ω-3 PUFA intake (30 mg/kg/day for 10 days) on expression and location of occludin in the aorta of ...

We give a simple proof of Chebotarëv’s theorem: Let p be a prime and ω a primitive pth root of unity. Then all minors of the matrix ( ω ij )p−1 i,j=0 are non-zero. Let p be a prime and ω a primitive pth root of unity. We write Fp for the field with p elements. In 1926, Chebotarëv proved the following theorem (see [3]): Theorem. For any sets I, J ⊆ Fp with equal cardinality, the matrix (ω )i∈I,j...

Definition 1.1 A probability distribution P on (Ω,F) is a function P : F → [0, 1] which is (i) normalized, i.e. P[∅] = 0 and P[Ω] = 1 (ii) additive, i.e. P [ ∪i Ai ] = ∑ i P[Ai] , where A1,A2, . . . is a collection of disjoint events, i.e. Ai ∩ Aj = ∅ for all i, j. The triple (Ω,F ,P) is called a probability space. For discrete Ω: F = P(Ω) and P[A] = ∑ω∈A P[ω] e.g. P[even number on a die] = P[2...

In this paper we consider uncountable classes recognizable by ω-automata and investigate suitable learning paradigms for them. In particular, the counterparts of explanatory, vacillatory and behaviourally correct learning are introduced for this setting. Here the learner reads in parallel the data of a text for a language L from the class plus an ω-index α and outputs a sequence of ω-automata s...

Stream automata (also called ω-automata) and ω-regular languages are of paramount importance in Computer Science and Logic. A coalgebraic treatment of these structures has not been given yet. We study a simple two-sorted setting where deterministic Muller automata can be cast as coalgebras, so that coalgebraic bisimilarity coincides with language equivalence. From this characterisation, we deri...