Despite the apparent simplicity, measuring the position of f0 peaks can produce unexpected results. In any model of intonation where the fundamental frequency is derived from both an intonation component and a segmental component (e.g. consonantal perturbations or the intrinsic f0 shifts of vowels), the measured peak position does not equal the peak of the intonation component. The difference c...

Given a perfect superposition of [Formula: see text] states on a quantum system of [Formula: see text] qubits. We propose a fast quantum algorithm for collapsing the perfect superposition to a chosen quantum state [Formula: see text] without applying any measurements. The basic idea is to use a phase destruction mechanism. Two operators are used, the first operator applies a phase shift and a t...

Let 0 < a < 1 and set Φ(t) = |t|, ∀ t ∈ R. Let 1 < p < ∞ and n ≥ 1. We prove that the superposition operator u 7→ Φ(u) maps the Sobolev space W (R) into the fractional Sobolev space W (R). We also investigate the case of more general nonlinearities. Résumé. Superposition avec des puissances sousunitaires dans les espaces de Sobolev. Pour 0 < a < 1, soit Φ(t) = |t|, ∀ t ∈ R. Soient 1 < p < ∞ et ...