Neoteric optical media for refractive index determination of gems and minerals

Refractive index determination of minerals and gems often requires their immersion in fluids with the same refractive index. However, these natural materials frequently have refractive indices above the ranges of common organic solvents. Most available high refractive index immersion materials are solid at room temperature, toxic, noxious, corrosive, carcinogenic, or any combination thereof. Since the physical properties of ionic liquids can be tuned by varying the cation and/or anion, we have developed immersion fluids for mineralogical studies which are relatively benign. We report here the syntheses of a range of ionic liquids ( many novel) based on the 1-alkyl-3-methylimidazolium cation, which all have refractive indices greater than 1.4, and can be used as immersion fluids for optical mineralogy studies. We further show that for a series of ionic liquids with the same anion, the refractive indices can be adjusted by systematic changes in the cation.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

High precision C-14 dating of Holocene peat deposits: A comparison of Bayesian calibration and wiggle-matching approaches

The chronologies of five northern European ombrotrophic peat bogs subjected to a large ANIS C-14 dating effort (32-44 dates/site) are presented here. The results of Bayesian calibration (BCal) of dates with a prior assumption of chronological ordering were compared with a Bayesian wiggle-match approach (Bpeat) which assumes constant linear accumulation over sections of the peat profile. Interpolation of BCal age estimates of dense sequences of C-14 dates showed variable patterns of peat accumulation with time, with changes in accumulation occurring at intervals ranging from 20 to 50 cm. Within these intervals, peat accumulation appeared to be relatively linear. Close analysis suggests that some of the inferred variations in accumulation rate were related to the plant macrofossil composition of the peat. The wiggle-matched age-depth models had relatively high chronological uncertainty within intervals of closely spaced 14 C dates, suggesting that the premise of constant linear accumulation over large sections of the peat profile is unrealistic. Age models based on the assumption of linear accumulation over large parts of a peat core (and therefore only effective over millennial timescales), are not compatible with studies examining environmental change during the Holocene, where variability often occurs at decadal to centennial time-scales. Ideally, future wiggle-match age models should be constrained, with boundaries between sections based on the plant macrofossil composition of the peat and physical-chemical parameters such as the degree of decomposition. Strategies for the selection of material for dating should be designed so that there should be enough C-14 dates to accurately reconstruct the peat accumulation rate of each homogeneous stratigraphic unit. (c) 2006 Elsevier Ltd. All rights reserved.