Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

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.     

Palladium-catalysed 5-endo-trig allylic (hetero)arylation

A palladium-catalysed intramolecular allylic (hetero)arylation strategy for the synthesis of fused cyclopentenes incorporated with all-carbon quaternary and spiro centres is described. The method is straightforward, shows broad scope, proceeds in synthetically useful yields, and provides a rare means to construct complex cyclopentanoids. The reaction is believed to involve a kinetically unfavourable 5-endo-trig carbocyclisation of the tethered (π-allyl)palladium system. Further, this method was successfully applied as the key step in the total synthesis of diterpene natural products taiwaniaquinone H and dichroanone.

A palladium-catalysed intramolecular allylic (hetero)arylation strategy for the synthesis of fused cyclopentenes incorporated with all-carbon quaternary and spiro centres is described.     

Synthesis and properties of azoles and their derivatives. 10. Synthesis of 3,5-diaryl-4-nitroisoxazoles

A method was proposed for the synthesis of 3,5-diaryl-4-nitroisoxazoles entailing the brominatian of potassium salts of the corresponding 3,5-diaryl-²-isoxazolinyl-4-nitronic acids. The method may be used for the conversions of both the trans and cis isomers of 3,5-disubstituted 4-nitro-²-isoxazolines.Communication 9, See [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 189–192, February, 1985.     

Spectrophotometric determination of Fe(II) in milligram solid samples

The analytical procedure of determination of Fe(II) in the presence of Fe(III) in milligram samples is proposed. A solid sample is dissolved in hydrochloric acid in argon atmosphere. Subsequently, the pH-value of the solution is fixed and Fe(III) complexed by phosphoric buffer. At the next step Fe(II) is oxidized by -molybdosilicic acid. Finally, the intensity of colouring caused by the reduced form of the acid is measured at the wavelength 770 nm. The proper treatment of the sample during oxidation, and immediately before, is decisive for the accuracy of the analysis. The method was verified by means of the analysis of synthetic magnetite. The theoretical content of Fe(II) was 24.12%, the determined one was 24.02 ± 0.10%. The method was applied to the determination of the homogeneity of an iron catalyst for ammonia synthesis.     

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.     

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.     

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.