Let f : X 99K X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n > 1. Suppose there is an embedded copy of P that is invariant under f , with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose f restricted to this line is given by z 7→ z, with resulting invariant circle S. We prove that if a ≥ b, then th...

Bubbling to the surface: Microscale gas bubbles can be generated in a microfluidic device by simultaneously injecting CO(2) and a dispersion of particles whose hydrophobicity increases as the pH value decreases. The CO(2) dissolves rapidly out of the bubbles, which shrink, and render the dispersion increasingly acidic. This drives the particles to the bubble surface where they form a type of "a...

Abstract—This paper studies piecewise constant circuits with an impulsive switch. Since vector field of the circuit equation is piecewise constant, the trajectories are piecewise linear : it is well suited for precise analysis. First, we consider the autonomous case. The switch is controlled by a state and the circuits can exhibit chaotic behavior. Second, we consider the non-autonomous case. T...

We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a forking-like notion for types of singleton elements. Theorem 0.1 (Superstability from categoricity). Let K be a (< κ)-tame AEC with amalgamation. If κ = iκ > ...

This thesis investigates the critical groups of McKay-Cartan matrices, a certain type of avalanche-finite matrix associated to a faithful representation γ of a finite group G. It computes the order of the critical group in terms of the character values of γ, and gives some restrictions on its subgroup structure. In addition, the existence of a certain Smith normal form over Z[t] is shown to imp...

play a significant role in the theory of functional equations. Some information on the applications of (1.1) and (1.2) in the determination of substructures of algebraical structures, in the theory of geometric objects and classification of near-rings and quasialgebras, can be found, for example, in [1–5] and in the recent survey paper [6]. At the 38th International Symposium on Functional Equa...

This paper deals with the boundary feedback control of a bar undergoing axial vibrations. The feedback force is applied to one end of the bar and it is proportional to its velocity. The problem is of fundamental interest in control theory, structural dynamics, and the development of quiet boundaries in fields like earthquake engineering and computational mechanics. The system is not self-adjoin...

We consider a random field (Xn)n∈Zd and investigate when the set Ah = {k ∈ Zd; ‖Xk‖ ≥ h} has infinite clusters. The main problem is to decide whether the critical level hc = sup{h ∈ R; P (Ah has an infinite cluster) > 0} is neither 0 nor +∞. Thus, we say that a percolation transition occurs. In a first time, we show that weakly dependent Gaussian fields satisfy to a wellknown criterion implying...