Thallium Determination at the Single Picomole per Liter Level by Flow‐Injection Differential‐Pulse Anodic Stripping Voltammetry

The flow‐injection differential‐pulse anodic stripping voltammetric (FI‐DP‐ASV) procedure has been developed for the determination of thallium concentration of the order of the single pM. Due to the analyte preconcentration at the electrode, DPASV is among the leaders in competition for achieving a detection limit as low as possible. The enrichment factor can be easily regulated by the duration of the preconcentration time. A DPASV measurement in a flow‐injection system enables the circulation of an analyzed sample and a medium exchange when preconcentration is completed. This approach ensures significant improvement of a background current. The measurements were performed in a cell of the wall‐jet type containing the mercury film electrode. One hour preconcentration was used for the determination of the lowest thallium concentrations. The developed method provides the opportunity to determine thallium in real environmental samples at the single pM level with the detection limit equal to 0.25 pM and RSD equal to 8.2%. This is by more than one order of magnitude better than the lowest detection limit reported in the literature (5 pM). Additionally, the medium exchange resulted in the improvement of the measuring accuracy, which was evidenced by the application of a certified reference material.     

Water solubilization,determination of the number of different types of single-wall carbon nanotubes and their partial separation with respect to diameters by complexation with eta-cyclodextrin

Complexation of single-wall carbon nanotubes with 12-membered cyclodextrins enables not only their solubilization in water but also their partial separation with respect to diameters and determination of the number of nanotube types on the basis of NMR spectra.     

The flow shop problem with time lags and separated setup times

This paper generalizes Khurana-Bagga's flow-shop model which involves separated setup times and time lags where no restrictions are imposed on the processing and setup times as well as start and stop lags. It solves the two machine case and provides and approximate solution for the multimachine case. It also shows that Khurana-Bagga's algorithm is restricted to a special case of the two machine problem.     

General relativity as a generalized Hamiltonian system

A rigorous setting for Dirac's generalized Hamiltonian dynamics in an infinite number of dimensions is presented. It is shown that the dynamical formulation of general relativity fits into this scheme.Work partially supported by GNFM-CNR.     

Accurate and sensitive analysis of triplet repeat expansions by capillary electrophoresis

The reliable genetic diagnostics of triplet repeat expansions by capillary electrophoresis (CE) remains technically challenging due to the properties of the repeated GC-rich sequences. The biased base composition of the analyzed sample as compared to the commonly used DNA size standards makes the precise repeat length determination questionable. The homologous allelic ladders improve the accuracy of the repeat length analysis significantly. Their use, however, is not devoid of other complications. In the approach we propose, the allelic ladders are used only to properly calibrate the commercially available standards which serve then as internal standards in reliable and economical repeat length determination. In this study, we have also analyzed factors that could possibly increase the sensitivity of mutant allele detection by increasing the overall amplification efficiency and long-to-short product ratio.     

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites--water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 μm) have been measured by ¹H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254–344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.     

Conditional moments of <Emphasis Type="Italic">q</Emphasis>-Meixner processes

We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the Meixner polynomials. Special cases of these processes are known to arise from the non-commutative generalizations of the Lévy processes.Mathematics Subject Classification (2000): 60J25Research partially supported by NSF grant #INT-0332062, by the C.P. Taft Memorial Fund, and University of Cincinnatis Summer Faculty Research Fellowship ProgramAcknowledgementPart of the research of WB was conducted while visiting the Faculty of Mathematics and Information Science of Warsaw University of Technology. The authors thank M. Boejko for bringing to their attention several references, to Hiroaki Yoshida for information pertinent to Theorem 4.3, and to M. Anshelevich, W. Matysiak, R. Speicher, P. Szabowski, and M. Yor for helpful comments and discussions. Referees comments lead to several improvements in the paper.     

Description of All Complex Geodesics in the Symmetrized Bidisc

Effective formulae are found for the complex geodesics in thesymmetrized bidisc. 2000 Mathematics Subject Classification32F45 (primary).