Regularity of the Extremal Solution of Some Nonlinear Elliptic Problems Involving the <Emphasis Type="Italic">p</Emphasis>-Laplacian

We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u ^* belongs to L ^∞(Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)). This work was partially supported by MCyT BMF 2002-04613-CO3-02.     

An efficient sensitivity computation strategy for the evolutionary structural optimization (ESO) of continuum structures subjected to self-weight loads

This work presents a modified version of the evolutionary structural optimization procedure for topology optimization of continuum structures subjected to self-weight forces. Here we present an extension of this procedure to deal with maximum stiffness topology optimization of structures when different combinations of body forces and fixed loads are applied. Body forces depend on the density distribution over the design domain. Therefore, the value and direction of the loading are coupled to the shape of the structure and they change as the material layout of the structure is modified in the course of the optimization process. It will be shown that the traditional calculation of the sensitivity number used in the ESO procedure does not lead to the optimum solution. Therefore, it is necessary to correct the computation of the element sensitivity numbers in order to achieve the optimum design. This paper proposes an original correction factor to compute the sensitivities and enhance the convergence of the algorithm. The procedure has been implemented into a general optimization software and tested in several numerical applications and benchmark examples to illustrate and validate the approach, and satisfactorily applied to the solution of 2D, 3D and shell structures, considering self-weight load conditions. Solutions obtained with this method compare favourably with the results derived using the SIMP interpolation scheme.     

The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

The aim of this paper is twofold: to prove, for L ¹-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L ¹.     

Near infrared spectroscopy in the study of polymorphic transformations

The potential of near infrared (NIR) spectroscopy for the characterization of polymorphs in the active principle of a commercial formulation prior to and after the manufacturing process was assessed. Polymorphism in active principles is extremely significant to the pharmaceutical industry. Polymorphic changes during the production of commercial pharmaceutical formulations can alter some properties of the resulting end-products. Multivariate curve resolution-alternating least squares (MCR-ALS) methodology was used to obtain the “pure” NIR spectrum for the active principle without the need to pretreat samples. This methodology exposed the polymorphic transformation of Dexketoprofen Trometamol (DKP) in both laboratory and production samples obtained by wet granulation. No polymorphic transformation, however, was observed in samples obtained by direct compaction. These results were confirmed using by X-ray powder diffractometry (XRD) and differential scanning calorimetry (DSC) measurements. Pure crystalline polymorphs of DKP were available in the laboratory but amorphous form was not, nevertheless the developed methodology allows the identification of amorphous and crystal forms in spite of the lack of pure DKP.     

N-propargylamides via the asymmetric michael addition of B-alkynyl-10-TMS-9- borabicyclo[3.3.2]decanes to N-acylimines

[Structure: see text] The asymmetric synthesis of N-propargylamides through Michael addition of the alkynylborane 1 to N-acylimines is reported. The N-acetylimines provide the best substrates for the process exhibiting high selectivity (56-95% ee) with predictable stereochemistry. In several cases, 5 crystallizes in essentially pure form (97-99% ee) and a single-crystal X-ray structure was also obtained for 5g (R1=R2=Me, R3=o-Cl-C6C4). The process regenerates 4 for its direct conversion back to 1 and facilitates the efficient recovery of the pseudoephedrine.     

A comparison of four protocols for the immobilization of an aptamer on graphite composite electrodes

We have performed a comparative study on four protocols for the immobilization of the thrombin aptamer on a graphite-epoxy composite electrode with the aim to identify the most practical method for designing the corresponding impedimetric aptasensor. The protocols included (a) physical adsorption, (b) avidin-biotin affinity interaction, (c) electrochemical activation and covalent bonding via amide groups, and (d) electrochemical grafting using 4-carboxybenzenediazonium coupling. The properties of the sensing surface were probed by electrochemical impedance measurements in the presence of the (ferri/ferro)hexacyanide redox couple. An increase in the interfacial charge transfer resistance (R_ct) was noted in all cases after the aptamer-thrombin interaction had occurred. The selectivity of the aptasensor over common serum proteins was also systematically investigated. Physical adsorption resulted in the lowest detection limit of the probe (4.5 pM), while avidin-biotin interaction resulted in highest selectivity and reproducibility exhibiting a 4.9 % relative standard deviation at pM thrombin concentration levels.

Colorimetric determination of iron in infant fortified formulas by sequential injection analysis

 A procedure is described for the colorimetric determination of iron in infant fortified formulas based on sequential injection analysis (SIA). Iron(III) complexation with thiocyanate is used as colour developing reaction. The system enables the determination of iron in the samples (after digestion by dry ashing and treatment with 0.2 mol/L nitric acid in the range of 0.50–20.0 mg/L, consuming 140 μL of the sample and 8 mg thiocyanate per determination. The reactor geometry and the adjustment of the ionic content of the calibration solutions is important for the accuracy of the results. A regression line according to the equation [Fe(III) (mg/L)]_SIA=−0.3(±0.4)+1.03(±0.04) [Fe(III) (mg/L)]_FAAS was obtained after comparative analysis of a set of 12 samples. The measurement rate was 34 s, thus allowing to analyze 100 samples per hour with a relative standard deviation lower than 2%. Received: 30 July 1996/Revised: 1 October 1996/Accepted: 4 October 1996     

Investigations into the Antifungal,Photocatalytic, and Physicochemical Properties of Sol-Gel-Produced Tin Dioxide Nanoparticles

Transmission electron microscopy (TEM), atomic force microscopy (AFM), X-ray diffraction (XRD), energy dispersive X-ray (EDX), scanning electron microscopy (SEM), diffuse reflectance spectroscopy (DRS), and Fourier transform infrared (FTIR) spectroscopy were applied to evaluate the tin dioxide nanoparticles (SnO₂ NPs) amalgamated by the sol-gel process. XRD was used to examine the tetragonal-shaped crystallite with an average size of 26.95 (±1) nm, whereas the average particle size estimated from the TEM micrograph is 20.59 (±2) nm. A dose-dependent antifun3al activity was performed against two fungal species, and the activity was observed to be increased with an increase in the concentration of SnO₂ NPs. The photocatalytic activity of SnO₂ NPs in aqueous media was tested using Rhodamine 6G (Rh-6G) under solar light illumination. The Rh-6G was degraded at a rate of 0.96 × 10⁻² min for a total of 94.18 percent in 350 min.     

Study of ε-caprolactone polymerization by NIR spectroscopy

Near-infrared (NIR) spectroscopy is proposed for the in-line quantitative and kinetic study of the polymerization of ε-caprolactone and eventually to facilitate real-time control of the manufacturing process. Spectra were acquired with a fibre-optic probe operating in transflectance mode immersed in the reactor. The NIR data acquired were processed using a multivariate curve resolution alternating least squares (MCR-ALS) algorithm. The proposed method allows calculation of the concentration and spectral profiles of the species involved in the reaction. The key point of this method is the lack of reference concentrations needed to perform the MCR-ALS method. The use of an extended spectral matrix using both process and pure analyte spectra solves the rank deficiency. The concentration profiles obtained were used to calculate a kinetic fitting of the reaction, but the method was improved by applying kinetic constraints (hard modelling). The rate constants of batches at different temperatures and the energy of activation for this reaction were calculated. Whenever possible, the hard modelling combined with the MCR-ALS method improves the fit of the experimental data: the results show good correlation between the NIR and reference data and allow the collection of high-quality kinetic information on the reaction (rate constants and energy of activation).     

On the analysis of conformational dynamics in polymers with several rotational isomers

The ability of different correlation functions to shed some light onto the conformational dynamics of an amorphous polymer has been analyzed. The study has been performed on a polyethylene model polymer, which has been simulated at decreasing temperatures towards its glass transition, via the molecular dynamics technique. Three rotational isomers are allowed by the considered torsional potential. The correlation times associated with the evaluated transition rates have shown to be Arrhenius in nature, with activation energies resulting basically from internal rotation barriers. Overall torsional autocorrelation functions have been calculated. We have observed that they are dominated by slow events. Alternatively, a set of torsional autocorrelation functions associated with every isomeric state has been evaluated. Stretched exponential fits lead to correlation times that display Vogel-Fulcher temperature dependence.