Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization

We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. Our results are valid for any quantizer with accuracy ε > 0 operating in the no-overload regime. The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited functions, we construct frame paths that terminate smoothly in the zero vector, that is, with an appropriate number of vanishing derivatives at the endpoint.     

Bohr's inequality for uniform algebras

We prove a uniform algebra analogue of a classical inequality of Bohr's concerning Fourier coefficients of bounded holomorphic functions. The classical inequality follows trivially.

     

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5

We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y₂BaNi_1-xZn_xO₅. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility χ( T ) ∼ C /(Θ + T ) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the “impurity” susceptibility ( T ) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by T ( T ) = C _imp 1 + T _imp / T . In the temperature range [100 mK, 1 K] the experimental data are well fitted by T ( T ) = A ln( T / T _c ), where T _c increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility ( T ) which suggests the existence of antiferromagnetic correlations at very low temperature. Received 17 July 2001     

Cucurbit[6]uril pseudorotaxanes: distinctive gas-phase dissociation and reactivity

Cucurbit[6]uril forms a doubly charged complex with 1,4-butanediammonium cation that is observed using electrospray ionization Fourier transform mass spectrometry. Such 1:1 complexes are not observed for the smaller cucurbit[5]uril, which forms a 2:1 ammonium:cucurbituril complex instead. The 1:1 complex with cucurbit[6]uril is difficult to fragment via collisional activation; when it does fragment, both breakup of the cucurbituril cage and loss of the amine are observed. Further, the complex reacts with tert-butylamine via slow adduction. In contrast, nonrotaxane analogues (such as doubly charged 2:1 complexes of either protonated 1,4-butanediamine or protonated ethylenediamine with cucurbit[6]uril) fragment via easy loss of the intact amine upon collisional activation and react with tert-butylamine via rapid displacement of the original amine. On the basis of stoichiometry, fragmentation behavior, and reactivity, we conclude that the doubly charged complex of cucurbit[6]uril with 1,4-butanediammonium is a gas-phase pseudorotaxane.     

Determination of average degree of polymerisation and distribution of oligosaccharides in a partially acid-hydrolysed homopolysaccharide: a comparison of four experimental methods applied to mannuronan

The average degree of polymerisation (DP) and distribution of oligosaccharides in partially acid hydrolysed mannuronans were quantitatively evaluated by 1H NMR, electrospray ionisation mass spectrometry (ESI-MS), micellar electrokinetic capillary chromatography with UV detection (MEKC-UV), and high-pressure anion-exchange chromatography with pulsed amperometric detection (HPAEC-PAD). Our investigation shows that 1H NMR, MEKC-UV and, in particular, HPAEC-PAD can be used as quantitative tools to aid the investigation of polysaccharide structure, function and synthesis. For the latter two techniques, especially, this represents a significant new development as it enables calculation of the quantity of individual oligomers of nominal DP by direct analysis of a defined oligomer mixture. Appropriate statistical averages of number and weight distributions were also calculated and found to fit very well to predicted Kuhn distributions that assume random depolymerisation.     

High-spin to low-spin relaxation kinetics in the [Fe(TRIM)2]Cl2 complex

A quasi-quantitative photo-induced low-spin (LS)-->high-spin (HS) conversion of FeII ions has been observed in the [Fe(TRIM)2]Cl2 complex by irradiating the sample with blue light (488 nm) at 10 K. The time dependence of the HS-->LS relaxation has been studied between 10 K and 44 K by means of magnetic susceptibility measurements. These relaxation curves could be satisfactorily fitted by mono-exponential decays including tunnelling effect except for temperatures below 30 K. The introduction of a distribution of vibrational frequencies into this model improved significantly the fits in the low-temperature range and gave a good agreement with the experimental data in the whole temperature range suggesting a multi-rate relaxation process in this complex.     

Détermination de traces de mercure dans les systèmes biologiques par activation de neutrons

Résumé Une méthode simple et rapide de détermination de traces de mercure est présentée utilisant l'activation de neutrons. Le mercure 197 sous forme de complexe (HgCl₄ ^2–) est retenu sur une résine échangeuse d'anion qui est comptée directement. La méthode est appliquée à des milieux biologiques très divers. Les échantillons contiennent des quantités de mercure allant de 10 p. p. b. à 200 p. p. m. La déviation standard dans ces cas est de ± 10%.

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Determination of traces of mercury in biological material by neutron activation

Summary A simple and rapid technique for the trace analysis of mercury by neutron activation is presented. The activated mercury, as an HgCl₄ ^2– complex, is retained on an anion exchange resin which is counted directly. Results obtained for biological samples containing 10 p. p. b. to 200 p. p. m. are given. In this range, results had a ± 10% standard deviation.

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Zusammenfassung Ein einfaches und rasches Verfahren zur Bestimmung von Spuren Quecksilber durch Neutronenaktivierung wurde beschrieben. Das aktivierte Quecksilber wird als HgCl₄ ^2– an einem Anionenaustauscherharz adsorbiert und seine Aktivität direkt gemessen. Biologische Proben mit 10 ppb bis 200 ppm Hg wurden analysiert. In diesem Bereich betrug die Standardabweichung ± 10%.