Photochemical degradation of blends of polystyrene and poly(2,6 -dimethyl-1,4-phenylene oxide)

Blends of polystyrene and poly(2,6-dimethyl-1,4-phenylene oxide) that cover the entire compositional range have been subjected to the action of singlet oxygen from microwave discharge, dye-sensitized reaction, and photochemical oxidation. With the applied analytical technique, which consisted of infrared (IR) analysis, including ATR technique and a spectroscopic method combined with chemical analysis for hydroperoxide groups, it was not possible to detect any effect of the singlet oxygen treatment. For that reason singlet oxygen does not appear to be important to the initiation of the photooxidation of these blends. In connection with photochemical oxidation the interaction observed between the two components probably involves energy transfer from PS to PPO. This interaction results in the enhancement of reactions in PPO that lead to greater carbonyl group formation and crosslinking. Simultaneously, the probability of chain scission in the PS is lowered with increased PPO content, found by determining the changes in the molecular weights.     

A continuous parametric shape model

In this paper we propose a flexible continuous parametric shape model for star-shaped planar objects. The model is based on a polar Fourier expansion of the normalized radius-vector function. The expected phase amplitudes are modelled by a simple regression with parameters having nice geometric interpretations. The suggestedgeneralized p-order model is an extension of first- and second-order Gaussian shape models, and in particular the Gaussian assumption is relaxed. The statistical analysis is straightforward, as demonstrated by an application concerning shape discrimination of two cell nuclei populations.     

Three-Body Recombination with Two-Channel Contact Interactions

We use a two-channel contact interaction model to describe a system of three identical bosons. The two-channel model quantitatively describes the phenomena of Feshbach resonance in agreement with the phenomenological expression relating scattering length to magnetic detuning. The model also has a finite effective range. We investigate finite range effects in three-body recombination. The simpler one-channel contact interaction model predicts a characteristic geometric scaling of minima in the recombination coefficient as a function of scattering length with scaling parameter 22.7. We show that this factor is reduced when the effective range is included. We compare calculations to experiment.     

Two-Channel Skyrme–Hartree–Fock Model for Bose–Einstein Condensate Near Feshbach Resonance

We apply a two-channel Skyrme–Hartree–Fock model to describe an atomic Bose–Einstein condensate near a Feshbach resonance. In this model the single-atom wave-function has two components corresponding to the two intrinsic states of the atom related to the Feshbach resonance. From the variational principle we derive the corresponding system of two coupled equations for the single-atom wave-function—a generalization of the Gross–Pitaevskii equation. We carry out an exploratory gaussian variational calculation and show that the two-component model can successfully describe the collapse of the condensate near a Feshbach resonance.     

Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.