Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity

We study from a numerical point of view a multidimensional problem involving a viscoelastic body with two porous structures. The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations. Its corresponding variational formulation gives rise to three coupled parabolic linear equations. An existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution.     

Vapour pressures,osmotic and activity coefficients for binary mixtures containing (1-ethylpyridinium ethylsulfate + several alcohols) at T = 323.15 K

Osmotic coefficients of binary mixtures containing several primary and secondary alcohols (1-propanol, 2-propanol, 1-butanol, 2-butanol, and 1-pentanol) and the pyridinium-based ionic liquid 1-ethylpyridinium ethylsulfate were determined at T = 323.15 K using the vapour pressure osmometry technique. From the experimental results, vapour pressure and activity coefficients can be determined. For the correlation of osmotic coefficients, the extended Pitzer model modified by Archer, and the modified NRTL (MNRTL) model were used, obtaining deviations lower than 0.017 and 0.047, respectively. The mean molal activity coefficients and the excess Gibbs free energy for the binary mixtures studied were determined from the parameters obtained with the extended Pitzer model modified by Archer.     

Development of a thermal desorption-gas chromatography–mass spectrometry method for determining personal care products in air

This study describes the development of a new analytical method for determining 14 personal care products (PCPs) – nine synthetic musks, four parabens and one insect repellent – in air samples. The method is based on active sampling on sorbent tubes and thermal desorption-gas chromatography–mass spectrometry analysis, and is rapid, sensitive and drastically reduces the risk of sample contamination. Three kinds of tubes and traps were tested, those filled with Tenax TA being the most suitable for this study. Method validation showed good repeatability and reproducibility, low detection limits (between 0.03 ng m⁻³ for DPMI and 12.5 ng m⁻³ for propyl paraben) and good linearity for all compounds. Stability during storage indicated that samples must be kept refrigerated at 4 °C and analysed within 1 week of collection. The applicability of the technique to real samples was tested in different indoor and outdoor atmospheres. The total PCP values for indoor air ranged from 135 ng m⁻³ in a pharmacy to 2838 ng m⁻³ in a hairdresser's, whereas the values for outdoor air ranged from 14 ng m⁻³ for a suburban environment to 26 ng m⁻³ for an urban environment. In general, the most abundant synthetic musks were galaxolide (5.9–1256 ng m⁻³), musk xylene (1.6–766 ng m⁻³) and tonalide (1.1–138 ng m⁻³). Methyl and ethyl paraben (2.4–313 ng m⁻³ and 1.8–117 ng m⁻³, respectively) were the most abundant parabens. Although thermal desorption methods have been widely used for determining volatile organic compounds, they are rarely used with semi-volatile compounds. This study thus demonstrates that the thermal desorption method performs well with semi-volatile compounds and, for the first time, that it can be used for determining PCPs.     

Ultrasound-assisted emulsification microextraction with simultaneous derivatization coupled to fibre optics-based cuvetteless UV-vis micro-spectrophotometry for formaldehyde determination in cosmetic samples

In this work, ultrasound-assisted emulsification microextraction in combination with fibre optics-based cuvetteless UV-vis micro-spectrophotometry has been proposed as a novel method for the determination of formaldehyde in water-based cosmetics such as shampoo, conditioner and shower gel. The use of a powerful cup-horn sonoreactor allows simultaneous extraction and derivatization of the samples without any pre-treatment. The type and volume of organic extractant solvent, need for a disperser solvent, sonication conditions (sonication time and amplitude), ionic strength and centrifuging time have been carefully studied. Matrix effects were also evaluated. The European official method for quantification of formaldehyde in cosmetic products was used for comparison purposes. An important improvement in sensitivity and sample throughput as well as miniaturization was achieved. A limit of detection of 0.02 μg g⁻¹ of formaldehyde and a repeatability expressed as relative standard deviation of 5.9% were obtained.     

Usefulness of parallel factor analysis to handle the matrix effect in the fluorescence determination of tetracycline in whey milk

The determination of tetracycline by fluorescence spectrophotometry in complex matrices has some difficulties, because the presence of other compounds in the matrix affects the analytical signal. In this work, the effect of some inorganic species that are present in whey milk on the fluorescence signal of tetracycline is studied using a D-optimal experimental design. Next, an experimental strategy is proposed in conjunction with Parallel Factor Analysis, PARAFAC, modeling that leads to suitably modeling the severe matrix effect in the determination of tetracycline in whey milk. A specific design is performed in such a way that the lack of trilinearity due to the effect of the presence of interferents on the signal is obviated. Then, ten test samples from three brands of milk, spiked with different quantities of tetracycline and measured in 2 days were analysed using this methodology (mean of the absolute value of the relative errors: 5.1%). The developed analytical method fulfils the property of trueness, the relative errors being, both in calibration and prediction, inside the interval set by Commission Decision 2002/657/EC at these concentration levels. Decision limits (CCα) at x₀ = 0 μg L⁻¹ and at x₀ = 100 μg L⁻¹ were 13.2 and 112.4 μg L⁻¹ respectively, for α = 0.05; whereas detection capabilities (CCβ) were 25.9 μg L⁻¹ and 124.4 μg L⁻¹ respectively for α = β = 0.05.     

Osmotic coefficients of binary mixtures of 1-butyl-3-methylimidazolium methylsulfate and 1,3-dimethylimidazolium methylsulfate with alcohols at T = 323.15 K

Measurements of osmotic coefficients of BMimMSO₄ (1-butyl-3-methylimidazolium methylsulfate) and MMimMSO₄ (1,3-dimethylimidazolium methylsulfate) with ethanol, 1-propanol, and 2-propanol at T = 323.15 K are reported in this work. Vapour pressure and activity values for the binary systems studied are obtained from experimental results. The osmotic coefficients are correlated using the extended Pitzer model modified by Archer and the modified NRTL (MNRTL) model. The standard deviations obtained with both models are lower than 0.013 and 0.060, respectively. The parameters obtained with the extended Pitzer model of Archer are used to calculate the mean molal activity coefficients and the excess Gibbs free energy of the binary mixtures.     

Ti‐Catalyzed Barbier‐Type Allylations and Related Reactions

Versatility of titanium : Titanocene(III) complexes catalyze Barbier‐type allylations, intramolecular crotylations (cyclizations), and prenylations of a wide range of aldehydes and ketones. These reactions take place at RT under mild conditions compatible with many functional groups; provide good yields of open‐chain and cyclic homoallylic alcohols, including heterocyclic derivatives; and can be conducted enantioselectively by using enantiomerically pure titanium catalysts.

     

Numerical analysis of a dual-phase-lag model involving two temperatures

In this paper, we numerically analyse a phase-lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one-dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution.     

Frame completions with prescribed norms: local minimizers and applications

Let \(\mathcal {F}_{0}=\{f_{i}\}_{i\in \mathbb {I}_{n_{0}}}\) be a finite sequence of vectors in \(\mathbb {C}^{d}\) and let \(\mathbf {a}=(a_{i})_{i\in \mathbb {I}_{k}}\) be a finite sequence of positive numbers, where \(\mathbb {I}_{n}=\{1,\ldots , n\}\) for \(n\in \mathbb {N}\). We consider the completions of \(\mathcal {F}_{0}\) of the form \(\mathcal {F}=(\mathcal {F}_{0},\mathcal {G})\) obtained by appending a sequence \(\mathcal {G}=\{g_{i}\}_{i\in \mathbb {I}_{k}}\) of vectors in \(\mathbb {C}^{d}\) such that ∥g _i ∥² = a _i for \(i\in \mathbb {I}_{k}\), and endow the set of completions with the metric \(d(\mathcal {F},\tilde {\mathcal {F}}) =\max \{ \,\|g_{i}-\tilde {g}_{i}\|: \ i\in \mathbb {I}_{k}\}\) where \(\tilde {\mathcal {F}}=(\mathcal {F}_{0},\,\tilde {\mathcal {G}})\). In this context we show that local minimizers on the set of completions of a convex potential P _φ , induced by a strictly convex function φ, are also global minimizers. In case that φ(x) = x ² then P _φ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn’s conjecture on the FOD.