Hexakis(adamantyltrimethylammonium) cyclooctasilicate tetratetracontahydrate

The title compound, 6C₁₃H₂₄N⁺·H₂Si₈O₂₀⁶⁻·44H₂O, belongs to the class of cyclosilicate hydrates, which structurally can be positioned between the zeosils and the clathrate hydrates. [Si₈O₁₈(OH)₂] cubes carrying six negative charges are located on crystallographic inversion centres and are surrounded by six adamantyltrimethylammonium cations.     

On incidence between strata of the Hilbert scheme of points on $$\mathbb{P}^{2}$$

The Hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated Hilbert series. In general, the precise inclusion relation between the closures of the strata is still unknown. Guerimand, Ph.D Thesis, Universite’de Nice, 2002 studied this problem for strata whose Hilbert series are as close as possible. Preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata. In this paper we present a new approach, based on deformation theory, to Guerimand’s result. This allows us to show that the technical condition is not necessary. Michel Van den Bergh is a director of research at the FWO.     

Near-infrared photoluminescence of lanthanide complexes containing the hemicyanine chromophore

The near-infrared luminescence properties of three (E)-N-hexadecyl-N′,N′-dimethylamino-stilbazolium tetrakis(1-phenyl-3-methyl-4-benzoyl-5-pyrazolonato) lanthanide(III) complexes are described. These three complexes, containing trivalent neodymium, erbium and ytterbium, respectively, show near-infrared luminescence in acetonitrile solution upon UV irradiation. Luminescence decay times have been measured. The complexes consist of a positively charged hemicyanine chromophore with a long alkyl chain and a tetrakis(pyrazolonato) lanthanide(III) anion. Because of the absence of an -hydrogen atom in the pyrazolonato ligands, and because of the saturation of the coordination sphere by four bidentate ligands, the luminescence properties are enhanced when compared to, e.g. quinolinate complexes.     

Efficient computation of characteristic roots of delay differential equations using LMS methods

We aim at the efficient computation of the rightmost, stability-determining characteristic roots of a system of delay differential equations. The approach we use is based on the discretization of the time integration operator by a linear multistep (LMS) method. The size of the resulting algebraic eigenvalue problem is inversely proportional to the steplength. We summarize theoretical results on the location and numerical preservation of roots. Furthermore, we select nonstandard LMS methods, which are better suited for our purpose. We present a new procedure that aims at computing efficiently and accurately all roots in any right half-plane. The performance of the new procedure is demonstrated for small- and large-scale systems of delay differential equations.     

Cobalt(II) Complexes of Nitrile‐Functionalized Ionic Liquids

A series of nitrile‐functionalized ionic liquids were found to exhibit temperature‐dependent miscibility (thermomorphism) with the lower alcohols. Their coordinating abilities toward cobalt(II) ions were investigated through the dissolution process of cobalt(II) bis(trifluoromethylsulfonyl)imide and were found to depend on the donor abilities of the nitrile group. The crystal structures of the cobalt(II) solvates [Co(C₁C_1CNPyr)₂(Tf₂N)₄] and [Co(C₁C_2CNPyr)₆][Tf₂N]₈, which were isolated from ionic‐liquid solutions, gave an insight into the coordination chemistry of functionalized ionic liquids. Smooth layers of cobalt metal could be obtained by electrodeposition of the cobalt‐containing ionic liquids.     

Two-dimensional simulation of the single-sided air-coupled ultrasonic pitch-catch technique for non-destructive testing

Non-contact air-coupled ultrasonic inspection of materials using single-sided access offers interesting possibilities for the development of in-line non-destructive testing (NDT) systems. This contribution reports observations and simulations obtained from a single-sided air-coupled pitch-catch configuration. The pitch-catch technique involves a set-up in which transmitter and receiver are located at the same side of the test object. Sound waves, reflected once or multiple times from the back-wall of the object or refracted by a discontinuity, are recorded and analyzed for visualization. The feasibility of the technique is demonstrated, experimentally, in the case of artificial defects in aluminium samples. Depending on the configuration one or more ultrasonic images of the defect can be observed, their number and relative position containing information about the location of the defect. The experiments are simulated using two distinctive methods. The first simulation is based on a ray tracing (shadow) approach, the second method uses a spectral solution implemented within Comsol. Both simulation methods allow simple prediction of the response images in experimental conditions with supplementary levels of complexity, which will assist the development and optimization of online inspection techniques.     

Application of fuzzy decision making to the fuzzy finite element method

In this paper we present a new approach to handle uncertainty in the Finite Element Method. As this technique is widely used to tackle real-life design problems, it is also very prone to parameter-uncertainty. It is hard to make a good decision regarding design optimization if no claim can be made with respect to the outcome of the simulation. We propose an approach that combines several techniques in order to offer a total order on the possible design choices, taking the inherent fuzziness into account. Additionally we propose a more efficient ordering procedure to build a total order on fuzzy numbers.