Let LS denote the language of (right) S-acts over a monoid S and let ΣS be a set of sentences in LS which axiomatises S-acts. A general result of model theory says that ΣS has a model companion, denoted by TS , precisely when the class E of existentially closed S-acts is axiomatisable and in this case, TS axiomatises E . It is known that TS exists if and only if S is right coherent. Moreover, b...

The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space Γ̈ = fZ+-valued Radon measures on Rdg. We show that under mild conditions, the set Γ̈\Γ is E-exceptional, where Γ is the space of locally finite configurations in Rd, that is, measures γ ∈ Γ̈ satisfying supx∈Rd γ(fxg) ≤ 1. Thus, the associated diffusion lives on the ...

Let LS denote the language of (right) S-acts over a monoid S and let ΣS be a set of sentences in LS which axiomatises S-acts. A general result of model theory says that ΣS has a model companion, denoted by TS , precisely when the class E of existentially closed S-acts is axiomatisable and in this case, TS axiomatises E . It is known that TS exists if and only if S is right coherent. Moreover, b...

The notion of a normal theory is introduced, and it is proved that for such a theory T, /(N„, 7") = 1 or 3e S(l. Wc also include a short proof of Lachlan's theorem that for superstable 7". /(X0, 7") = 1 or > N(1. (The property of normality is stronger than stability but incomparable to superstability.) 1. Preliminaries. We consider here theories T which are countable and complete (and of course...

Let G be a finite group. We consider the question: what are the superstable and co-stable abelian-by-G groups? (We consider these as structures in a suitable first order language, see § 1). We see that it is equivalent to ask: what are the superstable and co-stable Z[G]-modules? If we wish our answer to be such as to provide, at least in principle, some sort of uniform listing of all the (say) ...

This paper studies nonlinear dynamics of a simplified model of multiple-input parallel buck converters. The dynamic winnertake-all switching is used to achieve N-phase synchronization automatically, however, as parameters vary, the synchronization bifurcates to a variety of periodic/chaotic phenomena. In order to analyze system dynamics we adopt a simple piecewise constant modeling, extract ess...