Uniform convergence of basic Fourier–Bessel series on a q-linear grid

We study Fourier–Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The convergence results are illustrated with specific examples of expansions in q-Fourier–Bessel series.

     

Temperature dependent oxidative-induction time (TOIT) of irradiated and non-irradiated polypropylene—a new method

OIT's oxidation condition is very harsh for pure and irradiated polymers, particularly PP. PP undergoes pronounced molecular weight degradation in the course of processing and is prone to very fast oxidation and consequently very fast degradation, especially on samples submitted to previous aging and irradiation.

We developed a more useful method applicable by a much broader set of resins. Our group has recently introduced a new procedure to determine OIT, in non-stabilized and stabilized, irradiated and non-irradiated polypropylene. The new procedure was based on two main features: (1) starting the oxidation on melted samples at temperatures as low as possible; (2) oxidation under slow heating conditions. So each sample has a set of two values of time and temperature, as the new method is not isothermal any longer, so we better call it “Temperature dependent oxidative induction-time”. The new method showed itself as reproducible, sensitive to small changes in additive compositions and simple and inexpensive.     

Spectrophotometric determination of Blue Procion HEGN in effluents of textile industry exploiting the dye aggregation effect and flow injection analysis.

A new spectrophotometric method involving flow injection analysis and textile dye aggregation effect is proposed. The method is based on the aggregation effect of Blue Procion HEGN at pH 3, which relocates its maximum absorption wavelength from 620 to 776 nm, avoiding the interference of other blue textile dyes. For this task, a simple and robust flow injection system was designed, which became a very stable analytical method. When the system was applied to Blue Procion determination in effluent of textile industry, precise results were observed (RSD < 2% within 1.0 and 5.0 mg l(-1) HEGN). The analytical frequency was 80 measurements per hour; the analytical curve was linear from 1.0 to 5.0 mg l(-1) HEGN; the detection limit considering three times the standard deviation of the blank solution (n = 10) was estimated as 0.03 mg l(-1) HEGN; and recoveries between 95% and 105% were found. The system consumes 20 mg of sodium citrate and 125 microl of the sample per determination. No baseline drift was observed during extended (5 h) operation periods.     

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p≥3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete.     

Automatic stopped-flow determination of l-cysteine

An automatic stopped-flow method is proposed for the routine determination of microgram amounts of l-cysteine, based on its oxidation by 2,6-dichlorophenolindophenol (DPIP) in a weakly basic medium. The oxidation reaction is monitored by measuring the rate of the absorbance decrease at 615 nm, the wavelength of the maximum absorption for DPIP. Under optimal conditions, the calibration graph is linear over the range 2-32 mug/ml and the detection limit is 300 ng/ml. Most of the amino-acids tested have no effect on the rate of the oxidation reaction and are tolerated at high concentration levels. The sample throughput achieved, 80 samples per hr, allows the proposed method to be used for the routine determination of l-cysteine.     

Black hole particle emission in higher-dimensional spacetimes

In models with extra dimensions, a black hole evaporates both in the bulk and on the visible brane, where standard model fields live. The exact emissivities of each particle species are needed to determine how the black hole decay proceeds. We compute and discuss the absorption cross sections, the relative emissivities, and the total power output of all known fields in the evaporation phase. Graviton emissivity is highly enhanced as the spacetime dimensionality increases. Therefore, a black hole loses a significant fraction of its mass in the bulk. This result has important consequences for the phenomenology of black holes in models with extra dimensions and black hole detection in particle colliders.     

Studies in sigmatropic rearrangements of N-prenylindole derivatives--a formal enantiomerically pure synthesis of tryprostatin B

Rearrangement of N(a)-prenyl-N(b)-acetyltryptamine, induced by BF3.Et2O at low temperature, leads to a 2-prenyl derivative, and thence to the tricyclic tryptamine 7 and the indoline 8. Similarly, N(a)-prenyl-N(b)-phthaloyl-l-tryptophan methyl ester furnished the corresponding 2-prenyl derivative 16, a known advanced precursor of tryprostatin B. Density functional (B3LYP) calculations for the putative rearrangement transition state for N-prenylskatole show that prior coordination of BF3 to the indolic nitrogen changes the character of the subsequent sigmatropic pericyclic shifts from being entirely covalent to acquiring a significant degree of ionic character. The shifting prenyl group favours the endo over the exo mode of the transition state by 4.1 kcal mol(-1).