For a field K, rational function φ ∈ K(z) of degree at least two, and α ∈ P(K), we study the polynomials in K[z] whose roots are given by the solutions in K to φ(z) = α, where φ denotes the nth iterate of φ. When the number of irreducible factors of these polynomials stabilizes as n grows, the pair (φ,α) is called eventually stable over K. We conjecture that (φ, α) is eventually stable over K w...

We give a short and elementary proof of the theorem Lutz Weis that growth bound positive $C_0$-semigroup on $L_p(\mu)$ equals spectral its generator. In addition, we generalise result to case uniformly eventually semigroups.

We initiate a theory of locally eventually positive operator semigroups on Banach lattices. Intuitively this means: given initial datum, the solution corresponding Cauchy problem becomes (and stays) in part domain, after sufficiently large time. A drawback present C0-semigroups is that it applicable only when leading eigenvalue semigroup generator has strongly eigenvector. weaken requirement an...

When distributed clients query or update shared data, eventual consistency can provide better availability than strong consistency models. However, programming and implementing such systems can be difficult unless we establish a reasonable consistency model, i.e. some minimal guarantees that programmers can understand and systems can provide effectively. To this end, we propose a novel consiste...

We construct a Borel maximal eventually different family.