Rings of regular functions on nilpotent orbits and their covers

Summary LetG be a complex semisimple algebraic group with Lie algebra . Let be a nilpotentG-orbit, its ring of regular functions. We derive a formula for as aG-module and prove some partial results on a cover of . We then relate this formula to various existing multiplicity formulas forK-types in Harish-Chandra bimodules ofG.Supported by National Science Foundation Grant DMS-8505550     

Comparative tests to improve the gas chromatographic analysis of chlorobornanes in fish samples

A comparison was made between electron capture negative ionization quadrupole mass spectrometry (ECNI-MS) and electron capture detection (ECD) with regard to repeatability and reproducibility for the gas chromatographic (GC) analysis of toxaphene congeners [chlorobornanes (CHBs)]. The tests, including standard solutions and several cleaned fish extracts, showed larger relative standard deviations (RSDs) for the repeatability of ECNI-MS but no differences in the reproducibility of the 2 techniques. The sensitivity of the GC-ECNI-MS was considerably better than that of GC/ECD. Four stepwise-designed comparative tests were also conducted on GC analysis, cleanup, and the complete method. The results showed that, according to the current state-of-the-art, coefficients of variation for the between-laboratory performance were not < 20% and were usually between 20 and 30%. In spite of separation problems, e.g., for CHB 26, which cannot be separated into a single-component peak, a 95% methyl 5% phenyl polysiloxane (CP Sil 8) column was preferred to more polar columns for the analysis of CHBs 26, 40, 41, 44, 50, and 62. CHB 62 was more difficult to determine than CHB 26 and 50. Addition of the CHBs 40, 41, and 44 to the standard set of 3 chlorobornanes (26, 50, and 62) resulted in more separation problems. A 3-step cleanup method was recommended.     

Os(VIII)-catalysed oxidation of sulfides by sodium salt of N-chlorobenzenesulfonamide

Catalytic activity of Os(VIII) in the oxidation of some twenty organic sulfides with sodium salt of N-chlorobenzenesulfonamide (CAB) has been investigated in alkaline (pH8.7) t-butanol–water (1:1 v/v) medium. Significant retarding influence of [OH⁻] on the reactivity is exhibited. The catalysed reaction is strongly accelerated in the presence of Hg(II). Imperfections are observed in the linear Hammett relationship in the case of –NO₂ substituents.     

Bézout rings with almost stable range 1

Elementary divisor domains were defined by Kaplansky [I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949) 464-491] and generalized to rings with zero-divisors by Gillman and Henriksen [L. Gillman, M. Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82 (1956) 362-365]. In [M.D. Larsen, W.J. Lewis, T.S. Shores, Elementary divisor rings and finitely presented modules, Trans. Amer. Math. Soc. 187 (1) (1974) 231-248], it was also proved that if a Hermite ring satisfies (N), then it is an elementary divisor ring. The aim of this article is to generalize this result (as well as others) to a much wider class of rings. Our main result is that Bézout rings whose proper homomorphic images all have stable range 1 (in particular, neat rings) are elementary divisor rings.     

A field deployable method for a rapid screening analysis of inorganic arsenic in seaweed

Inorganic arsenic (iAs) in 13 store-bought edible seaweed samples and 34 dried kelp (Laminaria digitata) samples was determined by a newly developed, field-deployable method (FDM) with the aid of a field test kit for arsenic in water. Results from the FDM were compared to results from speciation analysis achieved by using high performance liquid chromatography coupled to inductively coupled plasma mass spectrometry (HPLC-ICP-MS). The FDM consisted of a simple extraction method using diluted HNO₃ to quantitatively extract iAs without decomposing the organoarsenicals to iAs followed by the selective volatilisation of iAs as arsine (AsH₃) and subsequent chemo-trapping on a filter paper soaked in mercury bromide (HgBr₂) solution. Method optimization with a sub-set of samples showed 80–94% iAs recovery with the FDM with no matrix effect from organo-arsenic species in the form of dimethylarsinic acid (DMA) on the iAs concentration. The method displayed good reproducibility with an average error of ±19% and validation by HPLC-ICP-MS showed that the results from the FDM were comparable (slope = 1.03, R² = 0.70) to those from speciation analysis with no bias. The FDM can be conducted within an hour and the observed limit of quantification was around 0.05 mg kg^?1 (dry weight). This method is well suited for on-site monitoring of iAs in seaweed before it is harvested and can thus be recommended for use as a screening method for iAs in seaweed.

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Graphical abstract Screening seaweed for their inorganic arsenic concentration within one hour without bias has been made possible in the field by using a field deployable arsenic kit. Its accuracy and precision was compared to HPLC-ICPMS.

     

Counting atoms in a deep optical microtrap

We demonstrate a method to count small numbers of atoms held in a deep, microscopic optical dipole trap by collecting fluorescence from atoms exposed to a standing wave of light that is blue detuned from resonance. While scattering photons, the atoms are cooled by a Sisyphus mechanism that results from the spatial variation in light intensity. The use of a small blue detuning limits the losses due to light-assisted collisions, thereby making the method suitable for counting several atoms in a microscopic volume.