A locking-free scheme for the LQR control of a Timoshenko beam

In this paper we analyze a locking-free numerical scheme for the LQR control of a Timoshenko beam. We consider a non-conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension. To solve the LQR problem we seek a feedback control which depends on the solution of an algebraic Riccati equation. An optimal error estimate for the feedback operator is proved in the framework of the approximation theory for control of infinite dimensional systems. This estimate is valid with constants that do not depend on the thickness of the beam, which leads to the conclusion that the method is locking-free. In order to assess the performance of the method, numerical tests are reported and discussed.     

Interaction of phenol and dopamine with commercial MWCNTs

We report the adsorption of phenol and dopamine probe molecules, from aqueous solution with NaCl, on commercial multiwall carbon nanotubes (MWCNT) and on their carboxylated derivative. The nanotubes were fully characterized by high resolution transmission electron microscopy (HRTEM), small angle X-ray scattering (SAXS), potentiometric titration, electrophoretic mobility, and nitrogen adsorption (77K) measurements. The experimental pollutant isotherms, evaluated using the Langmuir model, showed that only 8-12% and 21-32% of the BET surface area was available for phenol and dopamine, respectively, which is far below the performance of activated carbons. Influence of the pH was more pronounced for the oxidized MWCNT, particularly with dopamine. The strongest interaction and the highest adsorption capacity occurred at pH 3 with both model pollutants on both types of nanotubes. Although the surface area available for adsorption is far lower in MWCNTs than in activated carbons, it is nonetheless substantial. In particular, delayed release of toxic molecules that are either adsorbed on the surface or trapped in the inner bore of such systems could constitute an environmental hazard. The need for further adsorption studies with regard to their environmental aspects is therefore pressing, particularly for MWCNTs in their functionalized state.     

Improving quantitative gas chromatography-electron ionization mass spectrometry results using a modified ion source: demonstration for a pharmaceutical application

Gas chromatography-mass spectrometry is a well established analytical technique. However, mass spectrometers with electron ionization sources may suffer from signal drifts, hereby negatively influencing quantitative performance. To demonstrate this phenomenon for a real application, a static headspace-gas chromatography method in combination with electron ionization-quadrupole mass spectrometry was optimized for the determination of residual dichloromethane in coronary stent coatings. Validating the method, the quantitative performance of an original stainless steel ion source was compared to that of a modified ion source. Ion source modification included the application of a gold coating on the repeller and exit plate. Several validation aspects such as limit of detection, limit of quantification, linearity and precision were evaluated using both ion sources. It was found that, as expected, the stainless steel ion source suffered from signal drift. As a consequence, non-linearity and high RSD values for repeated analyses were obtained. An additional experiment was performed to check whether an internal standard compound would lead to better results. It was found that the signal drift patterns of the analyte and internal standard were different, consequently leading to high RSD values for the response factor. With the modified ion source however, a more stable signal was observed resulting in acceptable linearity and precision. Moreover, it was also found that sensitivity improved compared to the stainless steel ion source. Finally, the optimized method with the modified ion source was applied to determine residual dichloromethane in the coating of coronary stents. The solvent was detected but found to be below the limit of quantification.     

Pressure-amorphized cubic structure II clathrate hydrate: crystallization in slow motion

A range of techniques has so far been employed for producing amorphous aqueous solutions. In case of aqueous tetrahydrofuran (THF) this comprises hyperquenching of liquid droplets, vapour co-deposition and pressure-induced amorphization of the crystalline cubic structure II clathrate. All of these samples are thermally labile and crystallize at temperatures above 110 K. We here outline a variant of the pressure-amorphization protocol developed by Suzuki [Phys. Rev. B, 2004, 70, 172108], which results in a highly crystallization resistant amorphous THF hydrate. The hydrate produced according to our protocol (annealing to 180 K at 1.8 GPa rather than to 150 K at 1.5 GPa) does not transform to the cubic structure II THF clathrate even at 150 K. We track the reason for this higher stability to the presence of crystalline remnants when following the Suzuki protocol, which are removed when using our protocol involving higher pressures and an annealing step. These crystalline remnants later serve as crystallization seeds lowering the thermal stability of the amorphous sample. Our protocol thus makes a purely amorphous THF hydrate available to the research community. We use powder X-ray diffraction to study the process of nucleation and slow crystal growth in the temperature range 160-200 K and find that the local cage structure and periodicity of the fully crystalline hydrate develops even at the earliest stages of crystallization, when the "clathrate crystal" has a size of about two unit cells.     

New Aspects of the Maillard Reaction in Foods and in the Human Body

The reactions that occur during the cooking, baking, and preservation of foods of all kinds are of great importance for the production of aroma, taste, and color. However, more recently it has been shown that these reactions may be accompanied by a reduction in nutritive value and the formation of toxic compounds. For these reasons, the very complex reactions between reducing sugars and the free amino groups of amino acids or proteins, known as non-enzymatic browning or the Maillard reaction, have again caught the interest of chemists. The Maillard reaction came to be seen in a new light as it was realized that it actually occurred in the human body. As a general rule, the longer the half-life of a protein, the larger the amount of its Maillard products found, i.e., important factors are the ‘age’ or persistence of the protein in the body and the glucose concentration, particularly in diabetics. Many of the symptoms developed by diabetics resemble those of premature aging, which leads to the possibility that glucose, because of its reactivity towards proteins, is fundamentally involved in the normally slow progress of aging.     

An FPTAS for a single-item capacitated economic lot-sizing problem with monotone cost structure

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ɛ in time polynomial in the problem size and in 1/ɛ. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) production and backlogging cost functions. We omit concavity and convexity restrictions. Furthermore, we take advantage of a straightforward dynamic programming algorithm applied to a rounded problem.     

On Immediate Extensions of Ultrametric Spaces

The purpose of this paper is to define immediate extensions of ultrametric spaces with a totally ordered value set. It will be proved that an ultrametric space (X, d) with value set F is maximal if and only if it is pseudocomplete, i. e. any pseudoconvergent sequence of (X, d) has a pseudolimit in X. Every ultrametric space will be shown to possess a maximal immediate extension, but its uniqueness can only be obtained within the more specific class of essential extensions.