If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in X ∪ Y has a normal hyperdefinable X-internal subgroup N such that G/N is Y -internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developed. Moreover, a version of Schlichting’s Theorem for hyperdefinable fami...

Abstract Second-order mean-motion resonances lead to an interesting phenomenon in the sculpting of period-ratio distribution, due their shape and width period-ratio/eccentricity space. As osculating periods librate resonance, time-averaged period ratio approaches exact commensurability. The second-order increases with increasing eccentricity, thus more eccentric systems have a stronger peak at ...

In this article we show that the Baumslag-Solitar group BS(1, 2) is minimally almost convex, or MAC. We also show that BS(1, 2) does not satisfy Poénaru’s almost convexity condition P (2), and hence the condition P (2) is strictly stronger than MAC. Finally, we show that the groups BS(1, q) for q ≥ 7 and Stallings’ non-FP3 group do not satisfy MAC. As a consequence, the condition MAC is not a c...

In this paper we consider the commensurability of complex adaptive systems theory and actor-network theory to study co-evolutionary dynamics of IS emergence. We argue that the theories are defensible meta-theoretically when deployed from the philosophical position of critical realism. We provide a brief example drawn from a case study into the emergence of the phenomenon of research management ...

Light-induced forces can bind dielectric spheres into extended structures through two mechanisms, each with its own length scale which can be adjusted by the configuration of the external light source. By manipulating the commensurability of the two length scales, these two mechanisms can cooperate to bind a large number of spheres. When the two length scales become incommensurate for some part...

Using grand-canonical molecular dynamics simulations and free energy calculations of spherical molecular confined films, we investigate the internal energy and entropic origins of density layering and solvation force oscillations. We show that these properties, as well as diffusion and rheological characteristics of such films, depend on interfacial commensurability, with commensurate films exh...