Simultaneous determination of methyl- and ethyl-mercury by solid-phase microextraction followed by gas chromatography atomic fluorescence detection

A method for trace level determination of organomercury species in different biota matrixes by using aqueous-phase propylation followed by headspace solid-phase microextraction (HS-SPME) and gas chromatography (GC) coupled to pyrolysis-atomic fluorescence spectrometry (Py-AFS) detection has been optimized. To maximize peak area and symmetry factors of methylmercury (MeHg) and ethylmercury (EtHg) analyzed as propyl derivatives, carrier and make-up flow rates were optimized by a user-defined experimental design. A multiple response simultaneous optimization was applied using the desirability function to achieve global optimal operating conditions. They were attained at 2 and 6 mL min⁻¹ as carrier and make-up gas flow rates, respectively. In addition, pyrolyser temperature was also optimized, yielding the best value at 750 °C. Limits of detection and quantification at the optimum conditions were 0.04 ng g⁻¹ and 0.13 ng g⁻¹ for both, MeHg and EtHg. The developed analytical procedure was validated with a certified reference material (DORM-2) and applied to the determination of organomercury incurred in waterfowl egg and fish samples.     

Development of a methodology for the simultaneous determination of inorganic and organolead compounds using supercritical fluid extraction followed by gas chromatography-mass spectrometry and its application to environmental matrices

A method for the extraction of triethyl lead (TEL⁺), trimethyl lead (TML⁺), and Pb²⁺ from sand was developed using supercritical modified CO₂-CH₃OH extraction and in situ complexation with sodium diethyldithiocarbamate (NaDDTC) using a 2⁵ factorial exploratory design is described. The screened variables were (i) pressure (69-193 bar), (ii) temperature (40-150 °C), (iii) ligand amount (0-100 mg), (iv) methanol volume (0.0-0.5 mL) and (v) static time (0-45 min). The optimum extraction conditions found were as follow: pressure, 193 bar; temperature, 40 °C; amount of NaDDTC, 100 mg; methanol volume, 0.5 mL; static time 45 min; and CO₂ flow rate, 1 mL min⁻¹. Under these conditions the following recoveries were obtained (TML⁺ 97 ± 2%, TEL⁺ 70 ± 5%, and Pb²⁺ 100 ± 4%). The presence of NaDDTC is not necessary for the extraction of TML⁺ and TEL⁺, but it is a very significative parameter for Pb²⁺. A second experimental design 2² + star for temperature and pressure was realized, but the results were not better than those of the first model. SFE extract derivatization was achieved with pentylmagnesium bromide, and target analyte determination was carried out by gas chromatography-mass spectrometry. Detection limits in the full-scan mode were 4, 10, and 39 pg as lead for TMPeL, TEPeL and PbPe₄, respectively. The method was validated with urban dust containing TML⁺ (CRM 605. Pb 7.9 ±1.2 μg kg⁻¹) and river sediment containing inorganic lead (GBW08301. Pb 79.0 ± 12.0 mg kg⁻¹) as reference materials. The proposed method was applied to lead analysis in sand collected from an oil-polluted beach in Chile.     

Combined on-line transmission FTIR measurements and BTEM analysis for the kinetic study of a consecutive reaction in aqueous-organic phase medium

Combined on-line transmission FTIR spectroscopy and band-target entropy minimization (BTEM) analysis were employed in order to monitor and analyze the kinetics of the alkaline hydrolysis reaction of diethyl phthalate (DEP) in aqueous-ethanol solvent mixture. This reaction is irreversible and involves two consecutive steps with the formation of the observable mono-ion intermediate species. The pure component mid-FTIR spectra of the reactive species involved in this reaction, namely DEP, mono-ion intermediate and di-ion product were successfully reconstructed using BTEM. Their corresponding concentrations were also calculated and subsequently employed to derive the kinetic rate parameters. The effect of temperature and the solvent mixture compositions on these two consecutive reaction steps were also discussed. The temperature variation study showed that both reaction rate coefficients increased with temperature. Both rate coefficients were also affected by the solvent mixture compositions and reached minimum values at certain water-ethanol solvent composition (circa 60% (v/v)). This study shows the utility of combined on-line transmission FTIR spectroscopy and chemometric techniques for the present, rather complex, consecutive organic reaction. Moreover, the present type of approach could facilitate better understanding of a wide variety of organic reactions that are performed in aqueous and mixed aqueous-organic solvents.     

The Multivariate Integer Chebyshev Problem

The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in ℂ ^d . We study this problem on general sets but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert–Fekete upper bound for the integer Chebyshev constant, which depends on the dimension of space. In the case of single-variable polynomials in the complex plane, our estimate coincides with the Hilbert–Fekete result.      

An estimator of the tail index based on increment ratio statistics

In this paper, we introduce an increment ratio statistic (IR ^N,m ) based estimator for estimation of the tail index of a heavy-tailed distribution. For i.i.d. observations depending on the zone of attraction of an α-stable law (0 < α < 2), the IR ^N,m statistic converges to a decreasing function L(α) as both the sample size N and bandwidth parameter m tend to infinity. We obtain a rate of decay of the bias EIR ^N,m −L(α) and mean square error E(IR ^N,m −L(α))². A central limit theorem (IR ^N,m −EIR ^N,m )⟹ (0,σ²(α)) is also obtained. Monte Carlo simulations show that our tail index estimator has quite good empirical mean square error and, unlike the Hill estimator, is not so sensitive to a change of bandwidth parameter m. The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-25/08.     

Multivariate Bayesian process control for a finite production run

Most industrial products and processes are characterized by several, typically correlated measurable variables, which jointly describe the product or process quality. Various control charts such as Hotelling’s T², EWMA and CUSUM charts have been developed for multivariate quality control, where the values of the chart parameters, namely the sample size, sampling interval and the control limits are determined to satisfy given economic and/or statistical requirements. It is well known that this traditional non-Bayesian approach to a control chart design is not optimal, but very few results regarding the form of the optimal Bayesian control policy have appeared in the literature, all limited to a univariate chart design. In this paper, we consider a multivariate Bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent, normally distributed vectors of random variables. The problem is formulated in the POMDP (partially observable Markov decision process) framework and the objective is to determine a control policy minimizing the total expected cost. It is proved that under standard operating and cost assumptions the control limit policy is optimal. Cost comparisons with the benchmark chi-squared chart and the MEWMA chart show that the Bayesian chart is highly cost effective, the savings are larger for smaller values of the critical Mahalanobis distance between the in-control and out-of-control process mean.     

Improved prediction for a multivariate normal distribution with unknown mean and variance

The prediction problem for a multivariate normal distribution is considered where both mean and variance are unknown. When the Kullback–Leibler loss is used, the Bayesian predictive density based on the right invariant prior, which turns out to be a density of a multivariate t-distribution, is the best invariant and minimax predictive density. In this paper, we introduce an improper shrinkage prior and show that the Bayesian predictive density against the shrinkage prior improves upon the best invariant predictive density when the dimension is greater than or equal to three.     

Hessian orders and multinormal distributions

Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex cone of Hessian matrices, and we prove that if two random vectors are ordered by the Hessian order, then their means are equal and the difference of their covariance matrices belongs to the dual of . Then we show that the same conditions are also sufficient for multinormal random vectors. We study several particular cases of this general result.     

Cyclotomic factors of the descent set polynomial

We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when particular cyclotomic factors divide these polynomials. As an instance we deduce that the proportion of odd entries in the descent set statistics in the symmetric group Sn only depends on the number on 1's in the binary expansion of n. We observe similar properties for the signed descent set statistics.     

A class of multivariate copulas with bivariate Fréchet marginal copulas

In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Fréchet copulas. The coordinates of a random vector distributed as one of these copulas are conditionally independent. We prove that these multivariate copulas are uniquely determined by their two-dimensional marginal copulas. Some other properties for these multivariate copulas are discussed as well. Two applications of these copulas in actuarial science are given.