Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces

For discrete Hecke pairs (G,H), we introduce a notion of covariant representation which reduces in the case where H is normal to the usual definition of covariance for the action of G/H on c₀(G/H) by right translation; in many cases where G is a semidirect product, it can also be expressed in terms of covariance for a semigroup action. We use this covariance to characterise the representations of c₀(G/H) which are multiples of the multiplication representation on ?²(G/H), and more generally, we prove an imprimitivity theorem for regular representations of certain crossed products by coactions of homogeneous spaces. We thus obtain new criteria for extending unitary representations from H to G.     

Changes in glutathione and xanthophyll cycle pigments in the high light-stressed lichens Umbilicaria antarctica and Lasallia pustulata

Hydrated thalli of two lichen species--Umbilicaria antarctica and Lasallia pustulata--were exposed to high light (1800 micromol m-2s-1) for 30 min. High light exposure led to a decrease of total glutathione in both species, while de-epoxidation state of xanthophyll cycle pigments and non-photochemical quenching increased. In the subsequent recovery, the values of de-epoxidation state of xanthophyll cycle pigments decreased towards initial values. Glutathione (GSH) was resynthetised slowly. In conclusion, zeaxanthin-related protection is probably more involved than GSH-related protection in short-term response to high light stress in U. antarctica and L. pustulata. Faster recovery from photoinhibition in L. pustulata than U. antarctica is mainly due to faster conversion of zeaxanthin to violaxanthin and larger GSH pool of former species.     

The Transformation Groups Whose C*-Algebras are Fell Algebras

Let (G, X) be a locally compact transformation group in whichG acts freely on X. We show that the associated transformation-groupC*-algebra C₀(X) G is a Fell algebra if and only if X is aCartan G-space.     

Improving solid-state NMR dipolar recoupling by optimal control

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.     

Advanced method using microwaves and solid-phase microextraction coupled with gas chromatography-mass spectrometry for the determination of pyrethroid residues in strawberries

A microwave-assisted desorption method was developed and coupled with solid-phase microextraction and GC-MS for the analysis of pyrethroid residues in strawberries. In the first step, pyrethroid analytes were desorbed from the whole fruits in an aqueous acetonitrile solution at 50% under microwave assistance, so preventing these compounds to be captured with strong matrix effects by endogenous constituents. Then, the 100 microm poly(dimethylsiloxane)-coated fibre was exposed for 30 min in the obtained extracting solution. Calibration curves, realised from blank strawberries spiked at different concentrations with standards, showed a linear range between 1 microg/kg and 250 microg/kg with r2 > 0.992 and variation coefficients below 15%. Limits of detection and quantitation were found lower than 14 microg/kg and 40 microg/kg, respectively. Observed analysis results by using this method and relative to field incurred strawberry samples were also compared to those obtained by two accredited trading laboratories using traditional methods.     

Twisted actions and the obstruction to extending unitary representations of subgroups

Suppose that G is a locally compact group and π is a (not necessarily irreducible) unitary representation of a closed normal subgroup N of G on a Hilbert space . We extend results of Clifford and Mackey to determine when π extends to a unitary representation of G on the same space in terms of a cohomological obstruction.     

Temporal pitch mechanisms in acoustic and electric hearing

Two experiments investigated pitch perception for stimuli where the place of excitation was held constant. Experiment 1 used pulse trains in which the interpulse interval alternated between 4 and 6 ms. In experiment 1a these "4-6" pulse trains were bandpass filtered between 3900 and 5300 Hz and presented acoustically against a noise background to normal listeners. The rate of an isochronous pulse train (in which all the interpulse intervals were equal) was adjusted so that its pitch matched that of the "4-6" stimulus. The pitch matches were distributed unimodally, had a mean of 5.7 ms, and never corresponded to either 4 or to 10 ms (the period of the stimulus). In experiment 1b the pulse trains were presented both acoustically to normal listeners and electrically to users of the LAURA cochlear implant, via a single channel of their device. A forced-choice procedure was used to measure psychometric functions, in which subjects judged whether the 4-6 stimulus was higher or lower in pitch than isochronous pulse trains having periods of 3, 4, 5, 6, or 7 ms. For both groups of listeners, the point of subjective equality corresponded to a period of 5.6 to 5.7 ms. Experiment 1c confirmed that these psychometric functions were monotonic over the range 4-12 ms. In experiment 2, normal listeners adjusted the rate of an isochronous filtered pulse train to match the pitch of mixtures of pulse trains having rates of F1 and F2 Hz, passed through the same bandpass filter (3900-5400 Hz). The ratio F2/F1 was 1.29 and F1 was either 70, 92, 109, or 124 Hz. Matches were always close to F2 Hz. It is concluded that the results of both experiments are inconsistent with models of pitch perception which rely on higher-order intervals. Together with those of other published data on purely temporal pitch perception, the data are consistent with a model in which only first-order interpulse intervals contribute to pitch, and in which, over the range 0-12 ms, longer intervals receive higher weights than short intervals.     

Extending Fibre Nonlinear Interference Power Modelling to Account for General Dual-Polarisation 4D Modulation Formats

In optical communications, four-dimensional (4D) modulation formats encode information onto the quadrature components of two arbitrary orthogonal states of polarisation of the optical field. Many analytical models available in the optical communication literature allow, within a first-order perturbation framework, the computation of the average power of the nonlinear interference (NLI) accumulated in coherent fibre-optic transmission systems. However, all such models only operate under the assumption of transmitted polarisation-multiplexed two-dimensional (PM-2D) modulation formats, which only represent a limited subset of the possible dual-polarisation 4D (DP-4D) formats. Namely, only those where data transmitted on each polarisation channel are mutually independent and identically distributed. This paper presents a step-by-step mathematical derivation of the extension of existing NLI models to the class of arbitrary DP-4D modulation formats. In particular, the methodology adopted follows the one of the popular enhanced Gaussian noise model, albeit dropping most assumptions on the geometry and statistic of the transmitted 4D modulation format. The resulting expressions show that, whilst in the PM-2D case the NLI power depends only on different statistical high-order moments of each polarisation component, for a general DP-4D constellation, several other cross-polarisation correlations also need to be taken into account.     

Erratum to: “Aqueous Phenol and Ethylene Glycol Solutions in Electrohydrodynamic Liquid Bridging”

The original version of the article was published in Cent. Eur. J. Chem. 9(3) (2011), pp 391–403. Unfortunately, the original version of this article contains mistakes in the caption of the y-axis of Figs. 5,6 and 10 due to a font conversion problem. The actual units on the y-axis of these figures should be μS cm⁻¹, not mS cm⁻¹.