Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page

Commercial fire-retarded PET formulations - relationship between thermal degradation behaviour and fire-retardant action

Many types of fire-retardants are used in poly(ethylene terephthalate), PET, formulations, and two commercial fire retardants, Ukanol(TM) and Phosgard(TM), have been shown to improve significantly PET flame-retardancy when used as comonomers. Phosgard incorporates a phosphorus atom within the main chain whereas Ukanol incorporates a phosphorus atom as a pendent substituent. Despite their acknowledged effectiveness, the mode of action of these fire retardants remains unclear, and in this paper we present a comparison of the overall thermal degradation behaviour of PET and Ukanol and Phosgard fire retarded formulations. DSC and particularly TGA data show that both Ukanol and Phosgard have some stabilising influence on PET degradation, especially under oxidative conditions. TGA and pyrolysis experiments both clearly indicate that neither additive acts as a char promoter. Only the Phosgard formulation shows any release of volatile phosphorus species which could act in the gas phase. On the other hand, the most striking feature of the pyrolysis experiments is the macroscopic structure of the chars produced by the fire-retarded formulations, which hints at their fire-retardancy action - an open-cell charred foam was obtained upon charring at 400°C or 600°C. This foaming layer between the degrading melt and the flame would lower the amount of fuel available for combustion, and would also limit the feedback of heat to the condensed phase

Deformations of modules of differential forms

We study non-trivial deformations of the natural action of the Lie algebra $\mathrm{Vect}({\mathbb R}^n)$ on the space of differential forms on ${\mathbb R}^n$. We calculate abstractions for integrability of infinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation in the sense of \cite{ff}.Comment: Published by JNMP at http://www.sm.luth.se/math/JNM

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schr\"odinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schr\"odinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.Comment: 31 pages, 8 figures. Revised version. New title, new figure and new reference