On recognizing integer polyhedra

We give a simple proof that, determining whether a convex polytope has a fractional vertex, is NP-complete.Research supported by the National Science Foundation.     

Flow injection manifold for the direct spectrophotometric determination of bismuth in pharmaceutical products using Methylthymol Blue as a chromogenic reagent

A new simple and rapid flow injection method is reported for the direct determination of bismuth in pharmaceutical products. Methylthymol Blue (MTB) was used as a chromogenic reagent and the absorbance of the colored Bi(III)-MTB complex produced was monitored at 548 nm. The various chemical and physical variables were optimized and a study of interfering ions was also carried out. Linear calibration graphs were obtained from 0 to 100 mg l-1 Bi(m) (120 injections per hour). The precision was very good (sr = 1.3%) and the limit of detection was cL = 0.150 mg l-1. The average accuracy was also very good (er = 0.75%) and was evaluated by comparison of the results obtained with those claimed by the manufacturers. The method was found to be adequately selective, considering the ions that the samples contain.     

A simple model for calculating the compressibility of the transition-metal carbides and nitrides alloys ZrxNb1?xC and ZrxNb1?xN

The 4d-transition-metals carbides (ZrC, NbC) and nitrides (ZrN, NbN) in the rocksalt structure, as well as their ternary alloys, have been recently studied by means of a first-principles full potential linearized augmented plane waves method within the local density approximation. These materials are important because of their interesting mechanical and physical properties, which make them suitable for many technological applications. Here, by using a simple theoretical model, we estimate the bulk moduli of their ternary alloys Zr_xNb_1−xC and Zr_xNb_1−xN in terms of the bulk moduli of the end members alone. The results are comparable to those deduced from the first-principles calculations.     

Using clathrate hydrates for gas storage and gas-mixture separations: experimental and computational studies at multiple length scales

ABSTRACT

Clathrate hydrates have characteristic properties that render them attractive for a number of industrial applications. Of particular interest are the following two cases: (i) the incorporation of large amounts of gas molecules into the solid structure has resulted in considering hydrates as possible material for the storage/transportation of energy or environmental gases, and (ii) the selective incorporation of guest molecules into the solid structure has resulted in considering hydrates for gas-mixture separations. For the proper design of such industrial applications, it is essential to know accurately a number of thermodynamic, structural and transport properties. Such properties can either be measured experimentally or calculated at different scales that span the molecular scale-up to the continuum scale. By using clathrate hydrates as a particular case study, we demonstrate that performing studies at multiple length scales can be utilised in order to obtain properties that are essential to process design.     

Exploring an unknown graph

We wish to explore all edges of an unknown directed, strongly connected graph. At each point, we have a map of all nodes and edges we have visited, we can recognize these nodes and edges if we see them again, and we know how many unexplored edges emanate from each node we have visited, but we cannot tell where each leads until we traverse it. We wish to minimize the ratio of the total number of edges traversed divided by the optimum number of traversals, had we known the graph. For Eulerian graphs, this ratio cannot be better than two, and two is achievable by a simple algorithm. In contrast, the ratio is unbounded when the deficiency of the graph (the number of edges that have to be added to make it Eulerian) is unbounded. Our main result is an algorithm that achieves a bounded ratio when the deficiency is bounded. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 265–297, 1999     

Analytical and Structural Tools of Lipid Hydroperoxides: Present State and Future Perspectives

Mono- and polyunsaturated lipids are particularly susceptible to peroxidation, which results in the formation of lipid hydroperoxides (LOOHs) as primary nonradical-reaction products. LOOHs may undergo degradation to various products that have been implicated in vital biological reactions, and thus in the pathogenesis of various diseases. The structure elucidation and qualitative and quantitative analysis of lipid hydroperoxides are therefore of great importance. The objectives of the present review are to provide a critical analysis of various methods that have been widely applied, and more specifically on volumetric methods, applications of UV-visible, infrared, Raman/surface-enhanced Raman, fluorescence and chemiluminescence spectroscopies, chromatographic methods, hyphenated MS techniques, NMR and chromatographic methods, NMR spectroscopy in mixture analysis, structural investigations based on quantum chemical calculations of NMR parameters, applications in living cells, and metabolomics. Emphasis will be given to analytical and structural methods that can contribute significantly to the molecular basis of the chemical process involved in the formation of lipid hydroperoxides without the need for the isolation of the individual components. Furthermore, future developments in the field will be discussed.