f : ∪A → ρ is called a conflict free coloring of the set-system A (with ρ colors) if ∀A ∈ A ∃ ζ < ρ ( |A ∩ f−1{ζ}| = 1 ). The conflict free chromatic number χCF(A) of A is the smallest ρ for which A admits a conflict free coloring with ρ colors. A is a (λ, κ, μ)-system if |A| = λ, |A| = κ for all A ∈ A, and A is μ-almost disjoint, i.e. |A ∩ A′| < μ for distinct A,A′ ∈ A. Our aim here is to stud...

For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra At. The universal property of these coalgebras, resembling freeness, is that for every state s of every system S there exists a unique coalgebra homomorphism from a unique At which takes the root of t to s. Moreover, the tree coalge...

The existence of gravitational radiation arriving at null infinity J+, i.e., escaping from the physical system, is addressed in presence a non-negative cosmological constant Λ≥0. case with vanishing Λ well understood and relies on properties News tensor field (or function) defined J+. situation drastically different when Λ&gt;0, where there no known notion ‘News’ similar good properties. In thi...