Some remarks on the converse of Weyl’s conformal theorem

One of Weyl’s classical theorems states that a certain tensor, the Weyl tensor, is unchanged when the metric from which it is constructed is replaced by another metric conformally related to it. This paper explores the converse of this theorem.     

Kinetic Simulations of Atom Transfer Radical Polymerization (ATRP) in Light of Chain Length Dependent Termination

Kinetic simulations using the composite k_t model allows a better understanding of the effects of the persistent radical affecting ATRP or for that matter any activation–deactivation system. It also provides a better fit to experimental data in either bulk or solution conditions for ATRP polymerizations carried out at 110 °C. The results suggest that the composite model has broad utility over a wide range of experimental conditions and temperatures. The advantage of incorporating an accurate k_t model is that one can then use simulations as predictive tool to obtain polymers with higher chain‐end fidelity or polymers with low PDI values. This becomes important when attempting to use the chain‐ends for further functionalization to make complex polymer architectures. This model can also be used in simulations of miniemulsion or seeded emulsions to determine the effect of compartmentalization with particle size.

     

Application of multidimensional scaling to subjective evaluation of coded speech.

We present results from a pilot study directed at developing an anchorable subjective speech quality test. The test uses multidimensional scaling techniques to obtain quantitative information about the perceptual attributes of speech. In the first phase of the study, subjects ranked perceptual distances between samples of speech produced by two different talkers, one male and one female, processed by a variety of codecs. The resulting distance matrices were processed to obtain, for each talker, a stimulus space for the various speech samples. This stimulus space has the properties that distances between stimuli in this space correspond to perceptual distances between stimuli and that the dimensions of this space correspond to attributes used by the subjects in determining perceptual distances. Mean opinion scores (MOS) scores obtained in an earlier study were found to be highly correlated with position in the stimulus space, and the three dimensions of the stimulus space were found to have identifiable physical and perceptual correlates. In the second phase of the study, we developed techniques for fitting speech generated by a new codec under investigation into a previously established stimulus space. The user is provided with a collection of speech samples and with the stimulus space for these speech samples as determined by a large-scale listening test. The user then carries out a much smaller listening test to determine the position of the new stimulus in the previously established stimulus space. This system is anchorable, so that different versions of a codec under development can be compared directly, and it provides more detailed information than the single number provided by MOS testing. We suggest that this information could be used to advantage in algorithm development and in development of objective measures of speech quality.     

Estimation in integer‐valued moving average models

The paper presents new characterizations of the integer‐valued moving average model. For four model variants, we give moments and probability generating functions. Yule–Walker and conditional least‐squares estimators are obtained and studied by Monte Carlo simulation. A new generalized method of moment estimator based on probability generating functions is presented and shown to be consistent and asymptotically normal. The small sample performance is in some instances better than those of alternative estimators. Copyright © 2001 John Wiley & Sons, Ltd.     

The Supramolecular Assembly of Porphyrin Arrays

The self-assembly of porphyrin arrays containing three, seven or eleven porphyrins results from the interaction of the bis-pyridyl porphyrin 1 with the zinc porphyrins 2, 3, or 4, respectively.     

On the Control of the Fastest Growing Görtler Vortex

The response of the fastest growing linear G?rtler vortex to wall suction or blowing is investigated. The fastest growing mode occurs in flows of high local curvature and we show how its growth may be inhibited using very small amounts of suction or blowing. We show how the suction or blowing should be distributed in order to minimize the growth of a disturbance over a specified interval. Received 3 July 1996 and accepted 10 November 1998