We show that if G is a stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then G is superstable of finite U rank. Combined with recent work of Palaćın and Sklinos, we conclude that (Z,+, 0) has no proper stable expansions of finite weight. A corollary of this result is that if P ⊆ Zn is definable in a finite dp-rank expansion of (Z,+, 0), and (Z,+, 0,...

Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a map. We show that though such maps in general fall in the category of piecewise smooth maps, the mechanisms of bifurcations are quite different from those in ot...

Based on a classic paper by Ginibre [Commun. Math. Phys. 8, 26 (1968)] it is shown that, whenever Bogoliubov's approximation, that is, the replacement of a(0) and a*(0) by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of |a(0)|(2)/V and a*(0)a(0)/V in symmetry breaking fields, irrespective of the existence or absence of Bos...

We report the measurement of electromagnetically induced transparency (EIT) with Rydberg states in ultracold K40 Fermi gases, which is obtained through a two-photon process ladder scheme. Rydberg–EIT lines are by measuring atomic losses instead transmitted probe beam. Based on laser frequency stabilization locking to superstable cavity, we study line shapes for 37s and 35d states. experimentall...

Baizhanov and Baldwin [1] introduce the notions of benign and weakly benign sets to investigate the preservation of stability by naming arbitrary subsets of a stable structure. They connect the notion with work of Baldwin, Benedikt, Bouscaren, Casanovas, Poizat, and Ziegler. Stimulated by [1], we investigate here the existence of benign or weakly benign sets. Definition 0.1 1. The set A is beni...

In this paper we focus on a generalized Hénon–Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability properties to better understand the dynamics around these points. We show the conditions on the free parameters to have stability and we prove the superstable character of the origin for the classi...

We apply techniques from ω-stable and superstable groups to strongly connected and almost simple differential algebraic groups in the sense of Cassidy and Singer. We analyze differential algebraic group actions from this point of view, and prove several results regarding interpreting fields from these actions. We prove a differential algebraic analogue of Rienecke’s theorem. We show that every ...

We investigate the extent of second order characterizable structures by extending Shelah’s Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T . We show that all sufficiently large models of T have a characterization up to isomorphism in the extension of second order logic obtained by adding a little bit of infinitary logic if and only if...

This review paper studies nonlinear dynamics of parallel dc–dc converters and its practical applications. First, we introduce a single dc–dc converter which is a building block of the parallel system. Using a simple model of piecewise constant vector field, we show that the converters exhibit rich bifurcation phenomena including chaos and complicated superstable periodic orbits. We then introdu...