The geometry of sets of orthogonal frequency hypercubes

We extend the notion of a framed net, introduced by D. Jungnickel, V. C. Mavron, and T. P. McDonough, J Combinatorial Theory A, 96 (2001), 376–387, to that of a d‐framed net of type ?, where d ≥ 2 and 1 ≤ ? ≤ d‐1, and we establish a correspondence between d‐framed nets of type ? and sets of mutually orthogonal frequency hypercubes of dimension d. We provide a new proof of the maximal size of a set of mutually orthogonal frequency hypercubes of type ? and dimension d, originally established by C. F. Laywine, G. L. Mullen, and G. Whittle, Monatsh Math 119 (1995), 223–238, and we obtain a geometric characterization of the framed net when this bound is satisfied as a PBIBD based on a d‐class association Hamming scheme H(d,n). © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 449–459, 2007     

Symmetric designs and geometroids

A-setS in a symmetric 2-(v, k, ) design is a subset which every block meets in 0, 1 or points such that for any point ofS there is a unique block meetingS at that point only. Ovoids in three-dimensional projective spaces are examples of-secs. It is shown that if has a-set then is a geometroid withv=u ²+u+1 andk=u+1, whereu–1. The cases whenu is–1, and+1 are investigated and some open problems discussed.     

Determination of triclosan in human dental plaque by gas chromatography with atomic emission detection

A validated gas chromatographic method for the determination of triclosan in human dental plaque is described. Based on plaque sample weights of 10 mg, the limit of detection (2 × S/N) is 0.5 μg/g. The method is linear (r = 0.9986) from the limit of detection to 50 μg/g. Recoveries from placebos spiked with 2.0, 25, and 50 μg/g of triclosan were 105.6%±7.5%, 107.2%±3.1%, and 99.1%±1.1%, respectively (n = 3 at each level). Twenty replicate preparations and analyses of a homogenized sample, conducted by two operators over the course of 4 days, showed agreement to within 9% RSD. Analyses of dental plaque collected from patients after brushing with dental cream containing triclosan, shows triclosan to be retained in dental plaque at concentrations above the minimum inhibitory concentration (1 μg/g) after 12 h.     

Combined 1H NMR and DFT study of the solvent effects on the iron pentacarbonyl‐catalyzed photo‐assisted isomerization of allyl alcohol

The relative rates of iron pentacarbonyl‐catalyzed photo‐induced isomerization of allyl alcohol to propanal in various solvents have been measured using ¹H NMR spectroscopy. The reactions were run in linear and cyclic alkanes, alcohols, and amines in order to investigate solvent effects on the isomerization mechanism upon ultraviolet irradiation. The isomerization was efficient in nonane, hexane, cyclohexane, and benzene. The isomerization was very slow or completely suppressed in ethanol, propanol, isopropanol, triethylamine, and pyridine. Density functional theory calculations predicted thermodynamically favorable (ΔG^o < 0) formation of Fe(CO)₄–solvent compounds in the suppressing alcohol/amine solvents and unfavorable (ΔG^o > 0) formation in the hydrocarbon solvents. The strong solvent ligation likely prevents formation of Fe(CO)₃●(η²‐alkene) necessary for isomerization. Copyright © 2013 John Wiley & Sons, Ltd.     

A ‘poor man's Navier–Stokes equation’: derivation and numerical experiments—the 2‐D case

We present a systematic derivation of a discrete dynamical system directly from the two‐dimensional incompressible Navier–Stokes equations via a Galerkin procedure and provide a detailed numerical investigation (covering more than 107 cases) of the characteristic behaviours exhibited by the discrete mapping for specified combinations of the four bifurcation parameters. We show that this simple 2‐D algebraic map, which consists of a bilinearly coupled pair of logistic maps, can produce essentially any (temporal) behaviour observed either experimentally or computationally in incompressible Navier–Stokes flows as the bifurcation parameters are varied in pairs over their ranges of stable behaviours. We conclude from this that such discrete dynamical systems deserve consideration as sources of temporal fluctuations in synthetic‐velocity forms of subgrid‐scale models for large‐eddy simulation. Copyright © 2004 John Wiley & Sons, Ltd.