Two algorithms for the exchange lemma

Numerical Algorithms - In this note, we present two new algorithms for the Steinitz Exchange Lemma. They are grounded on a single application of a procedure (finding either a row echelon form or a...     

Thermotropic liquid crystal behaviour of gemini imidazolium-based ionic amphiphiles

Thermotropic ionic liquid crystals (LCs) are useful for a number of applications such as anisotropic ion transport and as organised reaction media/solvents because of their ordered fluid properties and intrinsic charge units. A large number of different ionic LC architectures are known, but only a handful of examples of gemini (i.e. paired or dimeric) ionic LCs have been prepared and studied. In this work, a series of 20 new symmetric, imidazolium-based, gemini cationic LCs containing two bridged imidazolium cations and two pendant alkyl chains was synthesised, and the thermotropic LC behaviours were characterised. The imidazolium unit provides a highly tunable and modular platform for the design and synthesis of gemini cationic LCs which offers excellent structure control. As expected, the thermotropic LC properties of these new amphilphilic, gemini ionic LCs were found to be strongly influenced by the length of the spacer between the imidazolium units, the length of the pendant alkyl tails, and the nature of the anion. Smectic A (SmA) thermotropic LC phases were observed in more than half of the gemini imidazolium LC systems studied.     

Speciation analysis of chromium in drinking water samples by ion-pair reversed-phase HPLC–ICP-MS: validation of the analytical method and evaluation of the uncertainty budget

The approach presented in this article refers to the modification of a method for the detection and quantitative determination of chromium species in water by high-performance liquid chromatography inductively coupled plasma mass spectrometry. The main aim of this work was to establish a detailed validation of the analytical procedure and an estimation of the budget of measurement uncertainty which was helpful in recognizing the critical points of the presented method. As a result of the method validation experiment, the obtained limit of quantification, repeatability and intermediate precision were satisfied for the quantification Cr(III) and Cr(VI) in water matrices. The trueness of the method was verified via an estimation of the recovery of the spiked real samples. The recovery rate of both determined analytes was found to be between 93 and 115 %. Considering that the validation of the method and the evaluation of measurement uncertainty are crucial for quantitative analysis, the above-mentioned assessment of the uncertainty budget was performed in two different ways: a modelling approach and a single-laboratory validation approach. The measurement uncertainties of the results were found to be 4.4 and 7.8 % for Cr(III), 4.2 and 7.9 % for Cr(VI) using the classical concept and method validation data, respectively. This paper is the first publication to presenting all the steps needed to evaluate the measurement uncertainty for the speciation analysis of chromium species. In summary, the obtained results demonstrate that the method can be applied effectively for its intended use.     

Stereoselectivity and kinetics of [4 + 2] cycloaddition reaction of cyclopentadiene to para‐substituted E‐2‐arylnitroethenes

In spite of diversified electrophilicity of E‐2‐arylnitroethenes, their [4 + 2] cycloaddition reactions with cyclopentadiene leads to the corresponding 6‐endo‐aryl‐5‐exo‐nitronorbornenes and 6‐exo‐aryl‐5‐endo‐nitronorbornenes as the only reaction products. Stereoselectivity, substituent and solvent effects, and activation parameters, suggest that these reactions occur via a synchronous concerted mechanism on both competing pathways. The experimental results obtained are consistent with the data from B3LYP/6‐31G(d) calculations. Due to high electrophilicity of E‐2‐arylnitroethenes, the reactions studied should be considered as polar [4 + 2] cycloadditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Simultaneous determination of Cd,Cr, Cu,Ni, Pb and Zn in sewage sludge by slurry introduction ICP-OES method

In order to evaluate the slurry nebulisation method as an alternative method for analysis of sewage sludge, the metal content of sludge samples of different origins was determined. The concentrations of six elements: Cd, Cr, Cu, Ni, Pb, and Zn were determined by introducing the sludge as a slurry into an inductively coupled plasma optical emission spectrometer (ICP-OES). Calibration was performed by using aqueous standard solutions. For comparison, the sewage sludge was also digested by microwave digestion and introduced into the plasma as an aqueous solution. The accuracy of the method was checked by analysing a sewage sludge certified reference material (CRM 007-040 Sewage Sludge). The Student's t-test showed that values obtained using slurry nebulisation were close to the certified values at a 95% confidence level. The values of elements Cd 11.1?±?0.8; Cr 37.7?±?3.3; Cu 563.3?±?38.4; Pb 119.2?±?10.1; Zn 729?±?68.2?mg?kg^?1 obtained using this method were comparable with those obtained using the conventional method. The slurry method can, therefore, be successfully applied to the determination of content of each element in sewage sludge with RSD less than 3%, without the need to predissolve them. This could avoid the use of hazardous chemicals, incomplete dissolution and loss of volatile analytes.     

A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama’s result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.     

Mössbauer effect and NMR studies of copper-cadmium ferrites

Hyperfine magnetic field distributions have been observed at room temperature in Cd _x Cu_1?x Fe₂O₄ (0≤x≤0.5) ferrites by the Mössbauer and NMR methods and are explained by statistical distributions of metallic ions separately within A and within B crystal sublattices.     

Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.