Kloosterman's uniformly distributed sequence

Applying the theory of uniform distribution, especially the Erdös-Turán-Koksma inequality and the Koksma-Hlawka inequality, to the two-dimensional Kloosterman sequence , j=1,2,…,?(n) (where , and ?(n) is the Euler function) we find an estimation for the discrepancy of this sequence and an error term for the Kth moment, K=1,2,…, of the sequence of distances as

     

Analysis of Silver Nanoparticles Using Single-Particle Inductively Coupled Plasma – Mass Spectrometry (ICP-MS): Parameters Affecting the Quality of Results

Single–particle analysis using inductively coupled plasma mass spectrometry offers a new tool for the characterisation of inorganic nanoparticles. Its development is connected with new generations of ultrafast spectrometers. This work is concerned with thorough investigation of parameters affecting the quality of the analysis of Ag nanoparticles, i.e., nanoparticle stability, transport efficiency and sensitivity of determination. The short-term stability of Ag nanoparticles in demineralised water can be prolonged to at least 7?h by the addition of 0.05% gelatin. The sensitivity was affected by plasma power and the nebuliser Ar flow. The transport efficiency decreased with increasing sample uptake, so a compromise between the efficiency and the total number of particles entering the spectrometer should be selected. The estimate of transport efficiency is distorted when more concentrated dispersions of nanoparticles are analysed because of the overlapping of signals of multiple nanoparticles. This effect was observed for dispersions of concentration greater than 1?×?10⁶?mL^?1 where an apparent decrease in transport efficiency from an initial value 7–8% to 1% was observed. The following parameters were found by method validation: concentration limit of detection of 97?mL^?1, nanoparticle diameter limit of detection 15?nm, linearity from 20 to at least 100?nm and repeatability of 1.3%. After validation, the method was applied to determine Ag nanoparticles in river water from the Vltava in Prague. Nanoparticles with diameters of 32–114?nm were found, and their number concentration increased from 340?mL^?1 to 1670?mL^?1 as the stream of water passed through urban agglomeration.     

(+)-(5R,6S)-2-(1′-Aminoalkyl)-6-(hydroxyalkyl)penem-3-carboxylic Acids

In continuation of our work on penem antibiotics, novel chiral (5R,6S)-2-(1′-aminoalkyl)-6-(hydroxyalkyl)-derivatives 1 have been synthesized by two essentially different strategies. Whereas the starting materials for 1a - f , azetidinones 2 and 5 , were obtained from chiral building blocks (6-aminopenicillanic acid and L-threonine, resp.), the one for 1g , azetidinone 9 , was derived from racemic 4-acetoxyazetidinone and, as chiral auxiliary, (2R)-2-mercaptopropan-1-ol. The 2-aminomethyl derivatives 1a (CGP 30 779) and 1f (CGP 31 608) proved the most potent compounds in the antibacterial tests in vitro and showed a well-balanced spectrum of activity by comparison with that of established β-lactams.     

L2‐estimates for the DG IIPG‐0 scheme

We discuss the optimality in L² of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity assumptions. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

Uncertainty of the concentration of a copper calibration solution

The postulated uncertainty of many commercially available standard solutions is estimated on the basis of uncertainties of individual preparation steps. The declared concentration of Cu standard solution (1000 ± 2) mg/L was verified by gravimetric analysis (found (1000.7 ± 0.4) mg/L), isotope dilution with commercial and laboratory-prepared isotope-enriched solutions (found (1000.6 ± 16.8) mg/L and (1002.4 ± 3.6) mg/L, respectively), and by atomic absorption spectrometry (found (1001.4 ± 5.3) mg/L). Uncertainty budgets of all used methods are given and the procedures of uncertainty estimation are fully documented.     

Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions

The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation error in the approximation of the nonlinear convective terms. The estimate of this error allows to analyse the error estimate of the method. The results obtained represent the completion and extension of the analysis from V. Dolej?í, M. Feistauer, Numer. Funct. Anal. Optim. 26 (2005), 349–383, where the truncation error in the approximation of the nonlinear convection terms was proved only in the case when the Dirichlet boundary condition on the whole boundary of the computational domain was considered.     

Custom-made interface between electrothermal vaporiser and inductively coupled plasma-mass spectrometer: determination of nickel by isotope dilution in plant samples

ICP-mass spectrometer Perkin Elmer Elan 6000 was adapted for ETV analysis by coupling with GBC GF 3000 graphite furnace atomiser. Both instruments were connected by a 25 cm long PTFE tubing of 6 mm i.d. and a custom-made interface. The apparatus was applied to nickel determination using isotope dilution technique. The efficiency of analyte transfer through the interface was approximately 20%, however the incomplete transfer did not influence the blank values. Measured isotope ratio was very stable, whereas the magnitude of ion signal showed a little shift. CRM samples were analysed after microwave decomposition and by slurry technique as well. Obtained results were compared with those of pneumatic sample nebulisation after nickel separation on Chelex column. All tested techniques gave accurate results with comparable precision. However, the slurry technique allowed significant decreasing of the blank values and the limit of detection. The duration of analysis run can also be substantially shortened from several hours to a few minutes.