Regularity of solutions of convolution equations

This paper investigates the regularity of solutions of convolution equations in the frame of classes of ultradifferentiable functions and ultradistributions. We improve previous work by Bonet, Chou, Fernández, Galbis, Meise and others.     

Trace analysis of parabens,triclosan and related chlorophenols in water by headspace solid-phase microextraction with in situ derivatization and gas chromatography–tandem mass spectrometry

An in situ derivatization solid-phase microextraction method has been developed for the determination of parabens, triclosan and related chlorophenols in water. Acetylated derivatives are selectively determined using gas chromatography with tandem mass spectrometry. Parameters affecting both derivatization and SPME procedures, such as fiber coating, extraction mode, temperature, volume of derivatizating reagent and ionic strength, are studied and optimized through a multifactorial experimental design. The performance of the method is studied in terms of accuracy, linearity, precision and limits of detection. Quantitative recoveries (≥82%) and satisfactory precision (RSD ≤ 12%) are obtained. Limits of detection at the low picogram per millilitre level are achieved for all target compounds. Linearity is studied in a wide range of concentrations and an analysis of variance with a lack-of-fit test is run to validate the calibration data. Extraction time profiles are also obtained. Finally, the applicability of the proposed method is demonstrated for several real samples including river water, wastewaters and swimming pool water. Since no matrix effects are observed, quantification can readily be carried out by external calibration with ultrapure water standards.     

Synthesis of core‐shell structured carboxylated microparticles with a straightforward procedure and their evaluation as a polymer support

Poly(trimethylolpropane trimethacrylate) microspheres with a narrow size distribution were obtained by precipitation polymerization. They were subsequently modified by surface grafting with acrylic acid in a polar ethanol–water reaction medium, without stabilizer, yielding core‐shell particles with diameters in the micrometer range. The resulting polymeric material was characterized by SEM and potentiometric titration, FTIR spectroscopy, and thermal analysis. It was shown that the particle characteristics (size, size distribution, and functionality) obtained by this straightforward procedure can be controlled by modifying the synthesis parameters (monomer concentration, agitation rate, and temperature). The high functionality, the chemical and physico‐mechanical stability, as well as the possibility to control the performances of the resulting polymeric materials by synthesis allow its applications in various areas. Envisaging separation and catalysis domains, Cu(II), Cd(II), and Cr(III) uptake capacity from aqueous solutions was investigated under noncompetitive conditions as a function of synthesized particle functionality, time, and pH range. It was also found that the addition of the carboxylated microparticles to polyethylene stabilized with α‐tocopherol improved the thermo‐oxidative behaviour of the polymeric material. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5889–5898, 2005     

Self-assembled low-molecular-weight gelator injectable microgel beads for delivery of bioactive agents

We report the preparation of hybrid self-assembled microgel beads by combining the low molecular weight gelator (LMWG) DBS-CONHNH₂ and the natural polysaccharide calcium alginate polymer gelator (PG). Microgel formulations based on LMWGs are extremely rare due to the fragility of the self-assembled networks and the difficulty of retaining any imposed shape. Our hybrid beads contain interpenetrated LMWG and PG networks, and are obtained by an emulsion method, allowing the preparation of spherical gel particles of controllable sizes with diameters in the mm or μm range. Microgels based on LMWG/alginate can be easily prepared with reproducible diameters <1 μm (ca. 800 nm). They are stable in water at room temperature for many months, and survive injection through a syringe. The rapid assembly of the LMWG on cooling plays an active role in helping control the diameter of the microgel beads. These LMWG microbeads retained the ability of the parent gel to deliver the bioactive molecule heparin, and in cell culture medium this enhanced the growth of human mesenchymal stem cells. Such microgels may therefore have future applications in tissue repair. This approach to fabricating LMWG microgels is a platform technology, which could potentially be applied to a variety of different functional LMWGs, and hence has wide-ranging potential.

We report microgel beads with diameters of ca. 800 nm based on interpenetrating networks of a low-molecular-weight gelator and a polymer gelator, and demonstrate their use as heparin delivery vehicles to enhance stem cell growth.     

Spatial and temporal diffusion-control of dynamic multi-domain self-assembled gels

The dynamic assembly of a pH-responsive low-molecular-weight gelator (LMWG) within the pre-formed matrix of a second LMWG has been achieved via diffusion of an acid from a reservoir cut into the gel. Self-assembly of the acid-triggered LMWG as it converts from micellar aggregates at basic pH into gel nanofibers at lower pH values can be both spatially and temporally controlled. The pH-responsive LMWG has an impact on the stiffness of the pre-formed gel in the domains in which it assembles. When low acid concentrations are used, LMWG assembly is transient – after the initial proton diffusion phase, the pH rises and disassembly occurs as the system equilibrates. Re-application of additional acid as ‘fuel’ can then re-assemble the LMWG network. Using glucono-δ-lactone (which slowly hydrolyses to gluconic acid) instead of HCl gives slower, more spatially-restricted assembly, and creates longer-lasting pH gradients within the gel. The presence of an agarose polymer gel network improves the mechanical strength of the gels and appears to slightly enhance the rate of proton diffusion. More sophisticated reservoir shapes can be cut into these more mechanically robust gels, enabling the creation of diffusion waves with different geometries, and hence different patterns of LMWG activation. Multiple reservoirs can be used to create overlapping proton diffusion waves, hence achieving differentiated pH patterns in the gel. Using acid diffusion in this way within gels is an intriguing and powerful way of dynamic patterning. The ability to temporally-evolve spatially-resolved patterns using biocompatible weak acids, and the change in rheological performance of the triggered domains, suggest potential future applications of this strategy in tissue engineering.

The assembly of a pH-sensitive LMWG within a pre-formed network of a second LMWG can be achieved by diffusing acids from pre-cut reservoirs, giving rise to patterned gels in which the rheological properties evolve with spatial and temporal control.     

Rheological and thermal properties of agarose aqueous solutions and hydrogels

In this article, we report on the rheological properties of agarose aqueous solutions and gels. Viscosity curves were determined for homogeneous agarose aqueous solutions at different temperatures (from 68 to 38 °C) to study the viscosity behavior as the systems undergo gelation. The gelation phenomenon of agarose solutions was also investigated by shear oscillation experiments and differential scanning calorimetry. The gelation and melting temperature as a function of agarose concentration were determined together with the gelation and melting enthalpies. The results obtained were interpreted using the two‐step model describing the gelation of agarose in water. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 322–328, 2008     

Bilevel multiplicative problems: A penalty approach to optimality and a cutting plane based algorithm

Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterised by the existence of two optimisation problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimisation problem. In this paper we focus on the class of bilevel problems in which the upper level objective function is linear multiplicative, the lower level one is linear and the common constraint region is a bounded polyhedron. After replacing the lower level problem by its Karush–Kuhn–Tucker conditions, the existence of an extreme point which solves the problem is proved by using a penalty function approach. Besides, an algorithm based on the successive introduction of valid cutting planes is developed obtaining a global optimal solution. Finally, we generalise the problem by including upper level constraints which involve both level variables.