Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC

In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the skew fields F=R,C,H. We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters. In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of K-biinvariant functions on G as special cases. The characters are given by the associated hypergeometric functions.     

Characterization and use of crystalline bacterial cell surface layers

Crystalline bacterial cell surface layers (S-layers) are one of the most common outermost cell envelope components of prokaryotic organisms (archaea and bacteria). S-layers are monomolecular arrays composed of a single protein or glycoprotein species and represent the simplest biological membranes developed during evolution. S-layers as the most abundant of prokaryotic cellular proteins are appealing model systems for studying the structure, synthesis, genetics, assembly and function of proteinaceous supramolecular structures. The wealth of information existing on the general principle of S-layers have revealed a broad application potential. The most relevant features exploited in applied S-layer research are: (i) pores passing through S-layers show identical size and morphology and are in the range of ultrafiltration membranes; (ii) functional groups on the surface and in the pores are aligned in well-defined positions and orientations and accessible for chemical modifications and binding functional molecules in very precise fashion; (iii) isolated S-layer subunits from a variety of organisms are capable of recrystallizing as closed monolayers onto solid supports (e.g., metals, polymers, silicon wafers) at the air–water interface, on lipid films or onto the surface of liposomes; (iv) functional domains can be incorporated in S-layer proteins by genetic engineering. Thus, S-layer technologies particularly provide new approaches for biotechnology, biomimetics, molecular nanotechnology, nanopatterning of surfaces and formation of ordered arrays of metal clusters or nanoparticles as required for nanoelectronics.     

Polydispersity Effects on the Demixing Behavior of Poly(Vinyl Methyl Ether)/Polystyrene Blends

Phase equilibrium calculations for solutions or mixtures of synthetic polymers become considerably more difficult when there is polydispersity of the polymers. To simplify the calculations, polydispersity is often neglected in the calculations or accounted for in a summary way only, and often only relatively simple free energy relations are applied. For example, Halary et al. published experimental demixing data on poly(vinyl methyl ether)/polystyrene blends. In evaluating the data the following assumptions were made: 1) the minimum of the demixing curve equals the critical point, 2) the X-parameter is independent of concentration and molecular weight, 3) the polydispersity may be roughly taken into account by using the formulas for monodisperse polymers and using the weight-average molecular weight. Continuous thermodynamics proves to be a suitable method to overcome the difficulties caused by polydispersity. Therefore, this method permits one to obtain detailed information on the phase equilibria in polymer solutions and in polymer blends in a relatively easy way. To show this, the data of Halary et al. are reanalyzed by means of continuous thermodynamics. In this way, more profound knowledge may be obtained from the experimental material, e.g., a more precise determination of the critical point and a more correct location of the spinodal.     

On list critical graphs

In this paper we discuss some basic properties of k-list critical graphs. A graph G is k-list critical if there exists a list assignment L for G with |L(v)|=k−1 for all vertices v of G such that every proper subgraph of G is L-colorable, but G itself is not L-colorable. This generalizes the usual definition of a k-chromatic critical graph, where L(v)={1,…,k−1} for all vertices v of G. While the investigation of k-critical graphs is a well established part of coloring theory, not much is known about k-list critical graphs. Several unexpected phenomena occur, for instance a k-list critical graph may contain another one as a proper induced subgraph, with the same value of k. We also show that, for all 2≤p≤k, there is a minimal k-list critical graph with chromatic number p. Furthermore, we discuss the question, for which values of k and n is the complete graph K_nk-list critical. While this is the case for all 5≤k≤n, K_n is not 4-list critical if n is large.     

Investigation of acidic pharmaceuticals in river water and sediment by microwave-assisted extraction and gas chromatography–mass spectrometry

Investigations were performed along the Danube river at Budapest (Hungary) by collecting water and sediment samples simultaneously for 1 year in order to clarify the possible hazard of selected acidic pharmaceuticals (ibuprofen, naproxen, ketoprofen, and diclofenac) on the water supply used for the production of drinking water by bank filtration. In the case of water samples, the sample preparation procedure included solid phase extraction (SPE), meanwhile, in the case of sediment samples, microwave-assisted extraction (MAE) followed by dispersive matrix extraction (DME) for pre-cleaning as well as SPE for enrichment. The quantification was carried out using gas chromatography–mass spectrometry (GC–MS). The calculated recoveries were 97–99% (± 7%) for the water and 95–103% (± 12%) for the sediment samples. In the river water, ketoprofen concentration was always below the limit of quantification (LOQ) level; ibuprofen, naproxen and diclofenac could be quantified in the range of 8–50, 2–30, 7–90 ng/L. In sediments, only naproxen and diclofenac were found in the range of 2–20 and 5–38 ng/g, respectively. According to the obtained results, the concentration ratios of the two phases linearly depended on the total organic carbon content (TOC) of the sediments at each sampling date. The linear regressions were 0.925 and 0.946 for naproxen and diclofenac, respectively.     

Gibbs free energy and equilibrium states in the Si/Si oxide systems

In this paper, the equilibrium states in the Si/Si oxide systems formed as a result of the phase separation of nonstoichiometric silicon oxide films are studied. The expressions for the Gibbs free energy of Si oxide and Si/Si oxide systems are derived thermodynamically. The transformations of the Gibbs free energy in the amorphous Si/Si oxide and the crystalline Si/Si oxide systems with the change in the amount of separated silicon and the composition of the silicon oxide phase are analyzed. By minimizing the Gibbs free energy of these systems, the equilibrium stoichiometry indices of silicon oxide are calculated as functions of its initial stoichiometry and the temperature. The solubility limits of Si in SiO(2) in equilibrium with amorphous and crystalline Si are determined. The obtained results form the basis for the development of a complete thermodynamic theory of phase separation in nonstoichiometric silicon oxide films with the formation of Si nanoinclusions in the silicon oxide matrix.     

High current density 3D electrodes manufactured by technical embroidery

Embroidery techniques allow flexible construction of 3D electrodes, which can form the conductive backbone in ultra-thick electrodes. 3D structures were manufactured by combination of stainless steel yarn, Cu wire, polyester (PES) fabric and Cu/Ni-coated PES web. Alkaline solutions of 9,10-anthraquinone-1,5-disulfonate or 1,2-dihydroxy-9,10-anthraquinone-3-sulfonate (Alizarin Red S) were used as reversible redox systems to characterise the electrodes by voltammetry in a flow cell. The height of the diffusion-limited current for the reversible cathodic reduction of the 9,10-anthraquinoide group was used as measure for the electrode performance. Compared to plane Cu electrodes, an increase in the diffusion-limited cathodic current density by factor 3–5 was obtained.