Indivisibility and Alpha-morphisms

Indivisibility and Alpha-morphisms

A relation R is p-divisible if for any partition of its basis into p + 1 subsets, R is embedded into the union of p of them. We prove that any countable p-divisible relation embeds two copies of itself intersecting in at most p− 1 elements. A relation R is indivisible if for any partition of its set of vertices into two subsets V1 and V2, there exists i ∈ {1, 2} such that R is embedded into R(V...

Age and weak indivisibility

Let H be a countable infinite homogeneous relational structure. If H is indivisible then it is weakly indivisible and if it is weakly indivisible then it is age indivisible. There are examples of countable infinite homogeneous structures which are weakly indivisible but not indivisible. It is a natural question to ask for examples of countable age indivisible homogenous structures which are not...

Indivisibility and Divisibility Polytopes

We study the the polytopes of binary n-strings that encode (positive) integers that are not divisible by a particular positive integer p | the indivisibility polytopes, as well as the more general \clipped cubes". Also, we discuss a potential application to factoring. Finally, we present some results concerning divisibility polytopes.

Indivisibility and Interdependence of Human Rights

Indivisibility of Electron Bubbles in Helium

A recent proposal by Maris[1], that single electron bubbles in helium might fission into separate, particle-like entities, does not properly take into account the failure of the adiabatic approximation when, due to tunneling, there is a long electronic time scale. The point along the fission pathway of a photoexcited p -state bubble, where the adiabatic approximation first breaks down, occurs w...