Definable nilpotent and soluble envelopes in groups without the independence property

We prove that in a group without the independence property a nilpotent subgroup is always contained in a definable nilpotent subgroup of the same nilpotency class. The analogue for the soluble case is also shown when the subgroup is normal in the ambient group.     

Fourier analysis of the Eulerian–Lagrangian least squares collocation method

A Fourier analysis was performed in order to study the numerical characteristics of the effective Eulerian–Lagrangian least squares collocation (ELLESCO) method. As applied to the transport equation, ELLESCO requires a C¹-continuous trial space and has two degrees of freedom per node. Two coupled discrete equations are generated for a typical interior node for a one-dimensional problem. Each degree of freedom is expanded separately in a Fourier series and is substituted into the discrete equations to form a homogeneous matrix equation. The required singularity of the system matrix leads to a ‘physical’ amplification factor that characterizes the numerical propagation of the initial conditions and a ‘computational’ one that can affect stability. Unconditional stability for time-stepping weights greater than or equal to 0-5 is demonstrated. With advection only, ELLESCO accurately propagates spatial wavelengths down to 2Δx. As the dimensionless dispersion number becomes large, implicit formulations accurately propagate the phase, but the higher-wave-number components are underdamped. At large dispersion numbers, phase errors combined with underdamping cause oscillations in Crank–Nicolson solutions. These effects lead to limits on the temporal discretization when dispersion is present. Increases in the number of collocation points per element improve the spectral behaviour of ELLESCO.     

Robustness of the extraction step when parallel factor analysis (PARAFAC) is used to quantify sulfonamides in kidney by high performance liquid chromatography-diode array detection (HPLC-DAD)

The robustness of a multiresidue method has been analysed for the extraction and quantification of sulfamethoxypyridazine, sulfamethoxazole and sulfadimethoxine in porcine kidney by HPLC-DAD through a Plackett-Burman design. Two experimental responses were examined, the mean recovery from three replicates (accuracy) and their standard deviation (precision). Three factors were tested: the volume of phosphoric acid (pH) added in the extraction step, the time used for passing the sample through the solid-phase extraction cartridge (flow rate) and methanol volume to elute the analytes from the cartridge. Due to the non-specificity of the chromatograms (unknown matrix interferences coelute with each sulfonamide) the PARAFAC model was employed to evaluate the concentration recovered in the experiments of the Plackett-Burman design as well as to identify the spectra of the substances according to the criteria set in the European Decision 2002/657/EC for the analysis of residues. The extraction step was concluded to be robust to the recovery and the standard deviation of all three analytes.     

Validation of an analytical method to determine sulfamides in kidney by HPLC-DAD and PARAFAC2 with first-order derivative chromatograms

Six sulfamides were extracted from kidney and analysed by high-performance liquid chromatography with diode array detection (HPLC-DAD): sulfadiazine, sulfamethazine, sulfamethoxypyridazine, sulfamethoxazole, sulfadimethoxine and sulfaquinoxaline.Two main difficulties arose in identifying and quantifying the analytes. Firstly, the chromatographic peaks of the matrix interferences overlapped with those of the analytes. The uniqueness property of PARAFAC2 solved this problem. Secondly, the gradient elution caused a baseline drift. The first-order derivative of the chromatograms minimized its effect.The analytical method was validated. As the performance criteria detailed in the European Decision 2002/657/EC are based on specific signals, this paper generalizes those criteria for higher-order and non-specific signals. In this sense the proposed methodology is general and can be applied to any chromatographic method (HPLC or GC) with a detector that provide a multivariate signal (MS, DAD, EC, etc.).     

Building robust calibration models for the analysis of estrogens by gas chromatography with mass spectrometry detection

Five hormonal growth promotants (diethylstilbestrol, hexestrol, dienestrol, 17-β-estradiol and 17-α-ethynylestradiol) have been analysed by gas chromatography with mass spectrometry detection (GC/MS, SIM mode) for four non-consecutive days. The aim is to build models with stable predictions. The strategies applied are internal standardization and global models carried out by gathering signals recorded on several days. Two models were examined: univariate models (with standardized peak area) and PARAFAC2 (the analyte scores were standardized by the scores of the internal standard). Internal standardization has been proved to be efficient for both models of dienestrol and ethynylestradiol. The mean relative error in absolute value when samples recorded on a different day to the calibration set are quantified by PARAFAC2 is 7.00% and 7.11% for dienestrol and ethynylestradiol, respectively. For diethylstilbestrol and estradiol, internal standardization was combined with global calibration models built with signals recorded under several sources of variability (different days). Thus predictions become steadier over time and in the estradiol example, errors decrease from 33.10% to 9.76%. The mean relative error in absolute value with PARAFAC2 updated models oscillates between 6.34% for ethynylestradiol and 10.74% for diethylstilbestrol. For univariate updated models errors range from 6.42% to 14.19% for ethynylestradiol and estradiol respectively. The combination of both strategies has been proved to be efficient independently of the analyte and of the signal order.     

Application of the Partial Least Square Technique to Identify Critical Variables in the Immunosorbent Manufacturing

The partial least square technique (PLS) was applied to the monoclonal antibody (Mab) CB.Hep-1 immunosorbent manufacturing to determine the influence of cyanate ester concentration, ligand concentration and target ligand density on Mab coupling efficiency, elution capacity, Hepatitis B surface antigen purity and ligand leakage (output variables). Results demonstrated that cyanate ester concentration, ligand concentration and density do not have an influence on output variables in assessed ranges. Conversely, the eluted antigen purity was significantly influenced by cyanate ester concentration and ligand concentration. In conclusion, the PLS application allows for the identification of critical variables and improvement of established chromatographic processes.     

Structural and luminescence characterization of synthetic Cr-doped Ni3(PO4)2

Ni_3–xCr_2x/3(PO₄)₂ (x=0 and 0.02) microcrystalline powders were obtained as single phases via a modified sol–gel Pechini-type in situ polymerizable complex method. The samples were characterized using scanning electron microscopy, X-ray diffraction, cathodoluminescence (CL), and thermoluminescence (TL) techniques. We found that Cr³⁺ doping modified the average particle and distribution. The mean particle size was 0.441 μm for Ni₃(PO₄)₂ and 0.267 μm for Ni_2.98Cr_0.013(PO₄)₂. The results also reveal that Cr³⁺ doping notably enhanced the CL and TL UV-blue emission.     

Usefulness of D-optimal designs and multicriteria optimization in laborious analytical procedures. Application to the extraction of quinolones from eggs

An analytical method has been developed to extract ciprofloxacin and enrofloxacin from eggs. The aim of this work is to determine the experimental conditions of extraction providing high recoveries with small standard deviations. An experimental design based on the D-optimality criterion and replicated three times was built to evaluate the effect of five factors related to the extraction which is the most inaccurate stage of the procedure. This non-classical design is needed because there are several practical constraints: (i) the extraction procedure is time-consuming, quinolones are not stable and the design must be performed in a single working session. (ii) The tube capacity of the centrifuge is 6, so the number of experiments will be 6 or a multiple of 6. In the optimal experimental conditions, the extraction is performed once with 5 ml of methanol. Then, fatty acids are removed with a mixture of hexane/ether. Analytes are finally separated and detected by HPLC-fluorescence without the additional step of purification by solid-phase extraction (SPE). Under these conditions, the mean recovery is 64% and 70% and the standard deviation 5% and 4% for ciprofloxacin and enrofloxacin, respectively. The capability of decision, CCalpha, is 3.1 and 2.8 microg kg(-1) of ciprofloxacin and enrofloxacin, respectively. The capability of detection, CCbeta, is 7.8 and 7.0 microg kg(-1) of ciprofloxacin and enrofloxacin, respectively. In both cases the probabilities of false positive, alpha, and of false negative, beta, were fixed at 0.05.