Estimates, decay properties, and computation of the dual function for Gabor frames

We present a simple proof of Ron and Shen's frame bounds estimates for Gabor frames. The proof is based on the Heil and Walnut's representation of the frame operator and shows that it can be decomposed into a continuous family of infinite matrices. The estimates then follow from a simple application of Gershgorin's theorem to each matrix. Next, we show that, if the window function has exponential decay, also the dual function has some exponential decay. Then, we describe a numerical method to compute the dual function and give an estimate of the error. Finally, we consider the spline of order 2; we investigate numerically the region of the time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.     

Analysis of Composites with Infrared Thermography

The aim of this study was a non-destructive evaluation of composites through their behaviour under thermal stimulation. Such behaviour was monitored by infrared thermography. Several specimens were fabricated involving: glass/epoxy with inclusion of foreign materials; carbon/epoxy with backdrilled holes; carbon/epoxy with impact damage; Glare^® failed in bearing way. The obtained results prove that infrared thermography is capable of detecting the materials inhomogeneities and/or damage listed above. In particular, lock-in thermography is capable of supplying useful information about: the distribution of the adhesive thickness in composite structures; the distribution of the paint thickness; the behaviour under load of aluminium layers and glass fibres in Glare^®.     

Strong reaction channels at barrier energies in the system 6Li + 208Pb

Large cross-section reaction channels were measured in the systems ⁶Li( ⁷Li) + ²⁰⁸Pb with high statistical accuracy at 5(3) energies around the Coulomb barrier from 29 to 39 MeV. These channels were assigned (mainly) to the breakup of ⁶Li, very loosely bound, into α + d and to the breakup of ⁵Li, produced by n-transfer to the target, into α + p and to similar processes with ⁷Li beam. The cross-sections with ⁶Li, S _α = 1.475 MeV, are systematically larger than the ⁷Li ones. This reflects, most likely, the higher binding energy of ⁷Li, S _α = 2.468 MeV. Theoretical predictions for the ⁶Li + ²⁰⁸Pb system which include for ⁶Li breakup to continuum states within a continuum discretized coupled-channels approach (CDCC) and resonant breakup plus n-transfer with DWBA reproduce the angular distribution shapes but still underestimate the cross-sections by a factor ∼ 3. Received: 15 January 2001 / Accepted: 3 March 2001     

MOVPE of II–VI materials

The development of II–VI MOVPE is reviewed, contrasting the narrow bandgap materials with the wide bandgap. Common issues are the need to grow the layers at lower temperatures than their III–V cousins in order to avoid point defects. This means that II–VI MOVPE occurs in a surface kinetic regime for precursor decomposition and has stimulated a lot of research on alternative precursors. The narrow bandgap II–VI growers have settled on dimethyl cadmium (DMCd) combined with diisopropyl telluride (DIPTe) and a liquid Hg source but wide bandgap growers are split between pyrolytic and photo-assisted growth. Recent progress in p-type doping has enabled the demonstration of some new devices, including two colour infrared detectors and the first MOVPE grown green emitting laser structure. The common theme appears to be hydrogen passivation of the Group V dopant and some novel precursor solutions to this problem are discussed.     

Voltammetry of pharmaceuticals using different types of modified electrodes

Summary Cyclic voltammetry was used to study the electrochemical behaviour of several chemically interesting drugs on different types of carbon based electrodes. The behaviours of the carbon paste and glassy carbon electrodes were investigated and compared with the results obtained with home-made new types of modified electrodes based on colloidal graphite or carbon black dispersed in a suitable polymer. The behaviour of the couple hexacyanoferrate-(II/ III) has been reported as a typical model of depolarizer. It has been shown that electrode responses were markedly influenced by the nature of the substrate. Performances of each electrode have been evaluated with regard to the shape of the voltammetric curves obtained during the investigation of these drugs.

---

Voltammetrie von Pharmazeutica mit Hilfe verschiedener Typen von modifizierten Elektroden

Zusammenfassung Das elektrochemische Verhalten mehrerer chemisch interessanter Pharmazeutica an verschiedenen Kohlenstoff-Elektroden wurde mit Hilfe der cyclischen Voltammetrie untersucht. Die Eigenschaften der Kohlenstoffpaste-Elektrode und der Glaskohlenstoff-Elektrode wurden geprüft und verglichen mit denjenigen von selbst hergestellten modifizierten Elektroden auf der Basis von kolloidalem Graphit und in einem geeigneten Polymer dispergiertem Ruß. Das Verhalten des Hexacyanoferrat(II/III)-Paares wurden als typisch für einen Depolarisator angesehen. Es konnte gezeigt werden, daß das Ansprechen der Elektrode von der Art des Substrats deutlich beeinflußt wird. Die Leistungsfähigkeit jeder Elektrode wurde an Hand der voltammetrischen Kurven der verschiedenen Pharmaca ausgewertet.

---

---

Thanks are expressed to the Fonds National de la Recherche Scientifique (F.N.R.S. Belgium) to one of us (G.J.P.) for partial support of this work.     

Weak choice principles

We consider several weak forms of the Axiom of Choice obtained debilitating some well known choice principles. Implication relations among them and independence results are established using, in some cases, permutation models or symmetric models. The relationship between Ramsey's Theorem and these choice principles is also explored, showing that, in this context, the known results are the best possible.

     

A New Shock Tube Facility for Tunnel Safety

In this paper, a new double diaphragm shock tube facility for studying the structural response of a circular plate resting on soil, when subjected to a shock wave, is described. The present shock tube has been designed in the framework of a more extensive research program aimed at the investigation of underground tunnel lining under blast and fire conditions. The innovative features of the facility are an end-chamber conceived to investigate soil-structure interaction and a burner equipment to heat the specimen in order to study to what extent thermal damage can affect the transmitted and reflected pressure wave as well as the structural response. Details of the shock tube design, construction and test procedure operations are discussed in the paper. Particular emphasis is placed on the principles that have driven the experimental equipment design choices. Numerical simulations have been performed to assess the ideal shock tube performance in terms of reflected pressure and test time duration as well as to evaluate how far the fire testing situation actually is from that normally used in tunnel design.     

High performance parallel numerical methods for Volterra equations with weakly singular kernels

Non-stationary discrete time waveform relaxation methods for Abel systems of Volterra integral equations using fractional linear multistep formulae are introduced. Fully parallel discrete waveform relaxation methods having an optimal convergence rate are constructed. A significant expression of the error is proved, which allows us to estimate the number of iterations needed to satisfy a prescribed tolerance and allows us to identify the problems where the optimal methods offer the best performance. The numerical experiments confirm the theoretical expectations.