Smoothness of subdivision surfaces at extraordinary points

A stationary subdivision scheme such as Catmull and Clark's is described by a matrix iteration around an extraordinary point. We show how higher order smoothness of a limiting surface obtained by a stationary subdivision algorithm for tri- or quadrilateral nets depends on the spectral properties of the matrix and give necessary and sufficient conditions. The results are also useful to construct subdivision algorithms for surfaces of any smoothness order at extraordinary points. This revised version was published online in August 2006 with corrections to the Cover Date.     

Precision spectroscopy at heavy ion ring accelerator SIS300

Unique spectroscopic possibilities open up if a laser beam interacts with relativistic lithium-like ions stored in the heavy ion ring accelerator SIS300 at the future Facility for Antiproton and Ion Research FAIR in Darmstadt, Germany. At a relativistic factor γ = 36 the ²P_1/2 level can be excited from the ²S_1/2 ground state for any element with frequency doubled dye-lasers in collinear geometry. Precise transition energy measurements can be performed if the fluorescence photons, boosted in forward direction into the X-ray region, are energetically analyzed with a single crystal monochromator. The hyperfine structure can be investigated at the ²P_1/2−²S_1/2 transition for all elements and at the ²P_3/2−²S_1/2 transition for elements with Z≤50. Isotope shifts and nuclear moments can be measured with unprecedented precision, in principle even for only a few stored radioactive species with known nuclear spin. A superior relative line width in the order of 5·10⁻⁷ may be feasible after laser cooling, and even polarized external beams may be prepared by optical pumping.     

The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.     

Ultrastructural types of alveolar macrophages in bronchoalveolar lavages from patients with pulmonary sarcoidosis

By routine applied quantitative BAL methods are particularly helpful for the diagnosis of pulmonary sarcoidosis. Here the morphology of the alveolar cells does not play a role. However, morphological and especially electron microscopic investigations might contribute to the clarification of the aetiology of this disease. In a prospective study we investigated the bronchoalveolar lavages (BALs) from 10 patients with recently histologically diagnosed, untreated pulmonary sarcoidosis. Commonly applied cytological and immunological BAL diagnostic techniques were accompanied by morphological investigations of alveolar cells, especially alveolar macrophages, using light and electron microscopy. All patients showed lymphocytic alveolitis with an increased number of CD4 positive lymphocytes as well as an increased CD4/CD8 ratio. A striking light microscopic finding was the great morphological variety of the alveolar macrophages. Electron microscopy revealed typical lymphocytes, neutrophils, and eosinophils as well as three different types of alveolar macrophages in all 10 patients: type I (approx. 30%) with a normal macrophage morphology, a vacuole-rich type II (approx. 30%) with myelin-like structures and type III (approx. 40%) with electron-dense inclusions. The occurrence of intracellular myelin figures in type II macrophages is a hint for increased phagocytotic processes of surfactant with or without its overproduction in the sense of a secondary alveolar proteinosis. Numerous electron-dense inclusions in type III also indicate an increased macrophage activity that leads to an increased release of cytokines, which in turn can trigger an inflammatory reaction.     

Stochastic modeling of experimental chaotic time series

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.     

Heterogeneously catalysed partial oxidation of acrolein to acrylic acid--structure, function and dynamics of the V-Mo-W mixed oxides

The major objective of this research project was to reach a microscopic understanding of the structure, function and dynamics of V-Mo-(W) mixed oxides for the partial oxidation of acrolein to acrylic acid. Different model catalysts (from binary and ternary vanadium molybdenum oxides up to quaternary oxides with additional tungsten) were prepared via a solid state preparation route and hydrochemical preparation of precursors by spray-drying or crystallisation with subsequent calcination. The phase composition was investigated ex situ by XRD and HR-TEM. Solid state prepared samples are characterised by crystalline phases associated to suitable phase diagrams. Samples prepared from crystallised and spray-dried precursors show crystalline phases which are not part of the phase diagram. Amorphous or nanocrystalline structures are only found in tungsten doped samples. The kinetics of the partial oxidation as well as the catalysts' structure have been studied in situ by XAS, XRD, temperature programmed reaction and reduction as well as by a transient isotopic tracing technique (SSITKA). The reduction and re-oxidation kinetics of the bulk phase have been evaluated by XAS. A direct influence not only of the catalysts' composition but also of the preparation route is shown. Altogether correlations are drawn between structure, oxygen dynamics and the catalytic performance in terms of activity, selectivity and long-term stability. A model for the solid state behaviour under reaction conditions has been developed. Furthermore, isotope exchange experiments provided a closer image of the mechanism of the selective acrolein oxidation. Based on the in situ characterisation in combination with micro kinetic modelling a detailed reaction model which describes the oxygen exchange and the processes at the catalyst more precisely is discussed.     

Silver aggregation caused by Stanna-closo-dodecaborate coordination: syntheses, solid-state structures and theoretical studies

Stanna-closo-dodecaborate [SnB11H11]2- reacts as a nucleophile with various silver electrophiles ([Ag(PMe3)]+, [Ag(PEt3)]+, [Ag(PPh3)]+, and Ag+) to form silver-tin bonds. Aggregation of two, three, or four units of [{Ag(SnB11H11)(PR3)}n]n- (PPh3, n = 2; PEt3, n = 3; PMe3, n = 4) was found, depending on the size of the coordinating phosphine. The structures of the silver-tin clusters in the solid state were determined by single-crystal X-ray diffraction. In these phosphine silver coordination compounds, the tin ligand exhibits micro2- and micro3-coordination with the silver atoms. From the reaction with silver nitrate, an octaanionic stanna-closo-dodecaborate coordination compound, [Et4N]8[Ag4(SnB11H11)6], was isolated. In this cluster, arranged as butterfly, the stannaborate shows various coordination modes at four silver atoms. In the reported silver-tin complexes, the silver-silver interatomic distances are in a range of 2.6326(10)-3.1424(6) A. Silver-tin distances were found between 2.6416(5) and 3.1460(6) A. Analysis of the molecular orbitals calculated by means of density functional theory shows that the LUMO of the core compound without [SnB11H11]2- units is always a totally symmetric combination of (mainly) s-orbitals of Ag atoms. This core is filled with electrons of the HOMOs of the [SnB11H11]2- units and is leading, in this way, to a stable compound.