Incomplete data problems in X-ray computerized tomography

Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4     

Tests of quantum electrodynamics using ion traps

Experiments in ion traps on the g factors for the free and the bound electron in low-Z, hydrogen-like ions have provided the most accurate tests of quantum-electrodynamics calculations. Moreover they have been used to determine new and precise values for fundamental constants. Extensions to more stringent tests using ions of higher values of the nuclear charge Z are on the way. Also other QED tests such as Lamb shifts or hyperfine structures in H-like ions using traps will be feasible in the near future. The tests in bound systems, however, will be limited by nuclear structure effects which are difficult to calculate. Assuming the QED calculations as correct, the experimental results may be used to determine nuclear contributions and thus support nuclear models. Contribution presented at the TCP06, Vancouver Island, 2006.     

Stochastic control problems with delay

We consider optimal control problems for systems described by stochastic differential equations with delay. We state conditions for certain classes of such systems under which the stochastic control problems become finite-dimensional. These conditions are illustrated with three applications. First, we solve some linear quadratic problems with delay. Then we find the optimal consumption rate in a financial market with delay. Finally, we solve explicitly a deterministic fluid problem with delay which arises from admission control in ATM communication networks.     

Native ethylene glycol in wine: Application of a dead volume free,very fast “deans heart-cut” system on-line with multi-chromatography

Data about the existence of native HO? CH₂? CH₂? OH (MEG) in natural wines and champagne has led to delicate questions because of legal decisions already made to declare wine or champagne illegal for sale if the MEG concentrations found are above 10 mg/liter. Action has been taken because of the DEG (diethylene glycol) disaster in European wines of 1985…86. An incorrect legal decision was made due to the belief that MEG cannot be produced biochemically by grape vines. A further reason may be lack of correct data on native MEG trace concentrations, as a result of the special behavior of this diol. As first member of a homologous series whose higher members (C₄) are normally found in all wines at quite high concentration levels, MEG shows extremely adsorptive behavior. The solution of the chromatographic problems is summarized in this paper. MEG concentrations in Riesling as example are in the range of 2 to 6 mg/liter and can easily be increased by biotechnological steps to a level of around 10 to 60 mg/liter. This is again due to the specific adsorptive behavior of MEG, which can be enriched on filter surfaces and displaced when the wine acidity changes with changing types. In order to control and guarantee the qualitative and quantitative results of MEG analyses we used a combination of Deans heart cutting on-line with Multi-Chromatography. It was easy to produce false data by many otherwise useful single column or two-dimensional separation processes, etc.     

Optical biosensor for pharmaceuticals, antibiotics, hormones, endocrine disrupting chemicals and pesticides in water: Assay optimization process for estrone as example

Certain contaminants at trace concentrations in surface waters can have dramatic effects on the hormonal system of organisms in the aquatic environment. Therefore, immunoanalytical methods at a very low limit of detection (LOD) and a low limit of quantification (LOQ) are becoming more and more important for environmental analysis and especially for monitoring drinking water quality. Environmental monitoring of antibiotics, hormones, endocrine disrupting chemicals, and pesticides in real water samples (e.g. surface, ground or drinking water) with difficult matrices places high demands on chemical analysis. Biosensors have suitable characteristics such as efficiency in allowing very fast, sensitive, and cost-effective detection. Here we describe an assay optimization process with a fully automated immunoassay for estrone which resulted in a LOD below 0.20 ng L⁻¹ and a LOQ below 1.40 ng L⁻¹. In contrast to common analytical methods such as GC-MS or HPLC-MS, the biosensor used requires no sample pre-treatment and pre-concentration. The very low validation parameters for estrone are the result of the continuous optimization of the immunoassay. The basis of our sensitive assay is the antibody with a high affinity constant towards estrone. During the optimization process, we reduced the amount of antibody per sample and improved the chip surface modification. Finally, this proceeding led to a calibration routine with an amount of antibody of only 3.0 ng per sample (sample volume: 1.0 mL). The reduction of the amount of antibody per sample results in better validation parameters (LOD, LOQ, and IC₅₀), but this reduction leads to the current device-related limitation of the River Analyser (RIANA).For some endocrine disrupting compounds, no effect levels (NOELs) in the lower nanogram per liter range are reported. This defines the challenge, which analytical methods have to compete with and our RIANA instrument with its improved sensitivity for the detection of a single hormone in the lower nanogram per liter range is a powerful tool in aquatic analytics in addition to the common analytical methods.     

Cyclisierungen unter beteiligung von fluoridionen. 2. Mitteil. [1], [2]. 4.5-perfluor-1.3-dioxolane

4.5-Perfluoro-1.3-dioxolanes $\text{2}$ are available by reaction of 2(α-chloroalkoxy)perfluoro-carbonyl halides $\text{3}$ or -ketone $\text{9}$ with fluoride ions. A mechanism for the intramolecular ring- closure-reaction is proposed. Hydrogen atoms at C-2 in $\text{2}$ can be exchanged photochemically by chlorine. Starting from the 2-monochloro-derivatives $\text{16}$ the 2-monofluoro-4.5-perfluoro- 1.3-dioxolanes $\text{18}$ are formed by reaction with triethylamine- hydrofluoride.     

The electron impact fragmentation of 3- and 4-styrylpyridazine

The electron impact mass spectrometric fragmentation of trans-3- and trans-4-styrylpyridazine is reported in detail, including a comparison with other aza-stilbenes. With regard to a distinction between the two isomeric styrylpyridazines, the intensity ratio of the M⁺ and [M-1]⁺ ions, the general degree of fragmentation and the elimination pathways of nitrogen proved to be most characteristic.