Proof of a conjecture on the supports of Wigner distributions

In this note we prove that the Wigner distribution of an f ∈ L₂(ℝ_n) cannot be supported by a set of finite measure in ℝ_2n unless f=0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ∈ L₂(ℝ_n) its Wigner distribution has a support of measure 0 or ∞ in any half-space of ℝ_2n.     

Terrain objects, their dynamics and their monitoring by theintegration of GIS and remote sensing

Geometrical and thematic data about terrain objects stored in a geographical information system (GIS) can be kept up-to-date by using remote sensing (RS) data. Geometrical and thematic data can be extracted from the RS data by segmentation and classification techniques respectively. The possibilities and reliability of the information extraction from RS data can be improved by the use of ancillary data and knowledge about the terrain objects. Object classification and aggregation hierarchies can be used to describe relationships between terrain objects; the categorization of the different types of terrain object dynamics that is presented will be based partly on these hierarchical relationships. Object models will be applied in a case study in which both the field geometry (field boundaries) and the crop type of agricultural fields are updated from a Landsat TM image. For that purpose, a three-stage strategy has been developed. In the first stage, the results of an edge detection procedure are integrated with fixed geometrical data already contained in the GIS by using knowledge about the aggregation structure and shape of the fields. In the next stage, the crop type of the fields is determined by means of object-based classification. Finally, conditional merging is performed to solve the problem of oversegmentation. The resulting field geometry was found to agree for 87% with the field geometry as determined by a photo-interpreter     

The elimination of fast variables in complex chemical reactions. III. Mesoscopic level (irreducible case)

The master equation for a complex chemical reaction cannot always be reduced to a simpler master equation, even if there are fast and slow individual reaction steps. Nevertheless the elimination of intermediates can be carried out with the help of the-expansion. This is illustrated with a well-known complex reaction: the dissociation of N₂O₅. It is shown that the intrinsic fluctuations in the N₂O₅ decay are larger than those implied by the master equation suggested by the macroscopic rate law.     

Fir laser stabilization using stark effect: Data on CH3Br and CH3Cl

Data on the influence of the Stark Effect on an optically pumped FIR laser with CH₃Cl or CH₃Br as active medium are given for various wavelengths. A very simple method for an effective FIR power stabilisation based on the Stark Effect is described. Its working is illustrated with the EPR signal of a 10% diluted DAG sphere.     

The effects of the column pressure drop on retention and efficiency in packed and open tubular supercritical fluid chromatography

The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available.     

Equilibrium of the reaction between dissolved sodium sulfide and biologically produced sulfur

The equilibrium of the heterogeneous reaction between dissolved sodium sulfide and biologically produced sulfur particles has been studied. Biologically produced sulfur was obtained from a bioreactor of a hydrogen sulfide removal process in which the dominating organism is Thiobacillus sp. W5. Detailed knowledge of this reaction is essential to understand its effect on the process. The results were compared with the equilibrium of the reaction of sulfide with ‘inorganic’ elemental sulfur. The equilibrium between dissolved sodium sulfide and biologically produced sulfur particles can be described by an equilibrium constant, K_x, which consists of a weighted sum of constants for polysulfide ions of different chain length, rather than a true single equilibrium constant. For biologically produced sulfur pK_x = 9.10 ± 0.08 (21 °C) and 9.17 ± 0.09 (35 °C) with an average polysulfide chain length x = 4.91 ± 0.32 (21 °C) and 4.59 ± 0.31 (35 °C). The pK_x value for biologically produced sulfur is significantly higher than for reaction of dissolved sodium sulfide with inorganic sulfur (pK_x = 8.82; 21 °C). This difference is probably caused by the negatively charged polymeric organic layer, which is present on biologically produced sulfur but absent with “inorganic” sulfur. Specific binding of polysulfide ions to the organic layer results in a higher polysulfide concentration at the reaction site compared to the bulk concentration. This results in an apparent decrease of the measured equilibrium constant, K_x.     

Development and validation of an analytical method for detection of estrogens in water

An analytical procedure enabling routine analysis of four environmental estrogens at concentrations below 1 ng L^–1 in estuarine water samples has been developed and validated. The method includes extraction of water samples using solid-phase extraction discs and detection by gas chromatography (GC) with tandem mass spectrometry (MS–MS) in electron-impact (EI) mode. The targeted estrogens included 17- and 17-estradiol (aE2, bE2), estrone (E1), and 17-ethinylestradiol (EE2), all known environmental endocrine disruptors. Method performance characteristics, for example trueness, recovery, calibration, precision, accuracy, limit of quantification (LOQ), and the stability of the compounds are presented for each of the selected estrogens. Application of the procedure to water samples from the Scheldt estuary (Belgium – The Netherlands), a polluted estuary with reported incidences of environmental endocrine disruption, revealed that E1 was detected most frequently at concentrations up to 7 ng L^–1. aE2 was detected once only and concentrations of bE2 and EE2 were below the LOQ.Presented at the 9th FECS Conference on Chemistry and the Environment, Bordeaux, France, 29 August–1 September 2004