RSOS Models and Jantzen–Seitz Representations of Hecke Algebras at Roots of Unity

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras H_m. We provide an explanation of this coincidence by showing how the irreducible H_m-modules which remain irreducible under restriction to H_{m_1} (Jantzen–Seitz modules) can be determined from the decomposition of a tensor product of representations sl_n.     

Magnetic resonance imaging: a new window into industrial processing.

Although the most important use of nuclear magnetic resonance imaging (MRI) continues to be for diagnostic medicine, recognition is being gained for many nonmedical applications. Examples include the following areas: petrogeology, food, agriculture, polymers and polymer-composites, and pharmaceuticals. These areas all involve studies of species that have short spin-spin relaxation times, and consequently need far fast gradient switching. These technical details are discussed and typical applications given.     

Properties of nonparametric estimators of autocovariance for stationary random fields

Summary We introduce nonparametric estimators of the autocovariance of a stationary random field. One of our estimators has the property that it is itself an autocovatiance. This feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters. Unlike estimators proposed recently by other authors, our own do not require assumptions such as isotropy or monotonicity. Indeed, like nonparametric function estimators considered more widely in the context of curve estimation, our approach demands only smoothness and tail conditions on the underlying curve or surface (here, the autocovariance), and moment and mixing conditions on the random field. We show that by imposing the condition that the estimator be a covariance function we actually reduce the numerical value of integrated squared error.     

Degradative chain transfer in vinyl acetate polymerizations using toluene as solvent

In this work, we propose that retardation in vinyl acetate polymerization rate in the presence of toluene is due to degradative chain transfer. The transfer constant to toluene (C_trs) determined using the Mayo method is equal to 3.8 × 10^?3, which is remarkably similar to the value calculated from the rate data, assuming degradative chain transfer (2.7 × 10^?3). Simulations, including chain‐length‐dependent termination, were carried out to compare our degradative chain transfer model with experimental results. The conversion–time profiles showed excellent agreement between experiment and simulation. Good agreement was found for the M_n data as a function of conversion. The experimental and simulation data strongly support the postulate that degradative chain transfer is the dominant kinetic mechanism. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3620–3625, 2007     

A local characterization of the johnson scheme

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod. Partial support provided by NSF (USA), SERC (UK), ZWO (NL).     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Effects of flanking band proximity, number, and modulation pattern on comodulation masking release

Comodulation masking release for a 700-Hz pure-tone signal was investigated as a function of the number and spectral positions of 20-Hz-wide comodulated flanking bands. In the first experiment, all stimuli were presented diotically. CMR was examined as a function of the number of flanking bands present, in conditions where the bands were arranged symmetrically around the signal frequency, were below the signal frequency, or were above the signal frequency. The number of flanking bands ranged from one to eight, and the magnitude of the diotic CMR ranged from approximately 5-16 dB. The results indicated: (1) bands closer to the signal resulted in larger masking release, and (2) more bands gave rise to larger CMR (but with diminishing returns above two flanking bands). Two additional sets of diotic conditions were examined and compared to the condition where all eight comodulated flanking bands were present: In one set of conditions, two of the eight flanking bands were removed; in the other set of conditions, two of the eight flanking bands were replaced with bands (termed "deviant" bands) that were not comodulated with respect to the other bands. There was very little effect of reducing eight bands to six, even when the removed bands were relatively near the signal frequency; however, CMR was substantially reduced when deviant bands were introduced, particularly when the deviant bands were placed relatively near the signal frequency. These reductions in CMR were slightly greater when each of the deviant bands had a unique modulation pattern (bideviant bands) than when the two deviant bands themselves shared the same modulation pattern (codeviant bands). In the second experiment, dichotic conditions were examined where the number and spectral positions of the flanking bands in the nonsignal ear were varied (the signal ear received only a 20-Hz-wide noise band centered on the signal frequency). The magnitude of the dichotic CMR ranged from approximately 2-10 dB, depending on condition. Effects of proximity and the number of flanking bands were similar to the effects obtained in diotic conditions. For both the diotic and the dichotic data, the effects of proximity were more consistent with an interpretation based upon across-channel processing than upon a within-channel interaction. The results obtained using deviant bands indicate that it is difficult for the auditory system to disregard the modulation pattern of flanking bands that differ from the modulation pattern of the on-signal band, particularly if such bands are proximal to the signal frequency.