On the asymptotic existence of Hadamard matrices

It is conjectured that Hadamard matrices exist for all orders 4t (t>0). However, despite a sustained effort over more than five decades, the strongest overall existence results are asymptotic results of the form: for all odd natural numbers k, there is a Hadamard matrix of order k²[a+blog₂k], where a and b are fixed non-negative constants. To prove the Hadamard Conjecture, it is sufficient to show that we may take a=2 and b=0. Since Seberry's ground-breaking result, which showed that we may take a=0 and b=2, there have been several improvements where b has been by stages reduced to 3/8. In this paper, we show that for all ?>0, the set of odd numbers k for which there is a Hadamard matrix of order k²2+[?log₂k] has positive density in the set of natural numbers. The proof adapts a number-theoretic argument of Erdos and Odlyzko to show that there are enough Paley Hadamard matrices to give the result.     

Ultra-high efficiency multilayer blazed gratings through deposition kinetic control

Diffraction efficiency of multilayer-coated blazed gratings (MBG) strongly depends on the perfection of the sawtooth-shaped layers in the overall composite structure. Growth of multilayers on sawtooth substrates should be carefully optimized to reduce groove profile distortion and, at the same time, to avoid significant roughening of multilayer interfaces. In this work, we report on a way to optimize growth of sputter-deposited Mo/Si multilayers on sawtooth substrates through variation of the sputtering gas pressure. We believe a new record for diffraction efficiency of 44% was achieved for an optimized MBG with groove density of 5250 lines/mm at the wavelength of 13.1 nm.     

Acetylation of dicarbonyl(η-cyclohexadiene)triphenyl- phosphineiron

Friedel-Crafts acetylation of dicarbonyl(η⁴-cyclohexadiene)triphenylphos-phineiron is accomplished in 96% yield under mild conditions to give dicarbonyl-(η⁴-5-endo-acetylcyclohexa-1,3-diene)triphenylphosphineiron. The structure of the product was established by direct comparison with the epimeric complex dicarbonyl(η⁴-5-exo-acetylcyclohexa-1,3-diene)triphenylphosphineiron produced by reaction of methyl magnesium iodide with dicarbonyl(η⁴-5-exo-cyanocyclohexa-1,3-diene)triphenylphosphineiron.     

Manipulating the enone moiety of levoglucosenone: 1,3-Transposition reactions including ones leading to isolevoglucosenone

The manipulation of the enone moiety associated with the biomass-derived, homochiral and now abundant compound levoglucosenone (1) is described. While the trichloroacetimidates derived from the allylic alcohols 3 and 4 failed to engage in Overman-type rearrangements, certain ester derivatives reacted in the presence of Pd[0]-catalysts to give regio-isomeric mixtures of β,γ-unsaturated malonates or ketones, the structures of which were confirmed by single-crystal X-ray analyses. In other sequences involving 1,3-transposition reactions, an operationally simple means for converting compound 1 into isolevoglucosenone (2) is described.

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Slow anion exchange,conformational equilibria,and fluorescent sensing in venus flytrap aminopyridinium-based anion hosts

The synthesis, anion binding, and conformational properties of a series of 3-aminopyridinium-based, tripodal, tricationic hosts for anions are described. Slow anion and conformational exchange on the (1)H NMR time scale at low temperature, coupled with NMR titration, results in a high level of understanding of the anion-binding properties of the compounds, particularly with respect to significant conformational change resulting from induced fit complexation. Peak selectivity for halides, particularly Cl(-), is observed. The approach has been extended to dipodal and tripodal podands based on 3-aminopyridinium "arms" containing photoactive anthracenyl moieties. The 1,3,5-tripodal host shows a remarkable selectivity for acetate over other anions, in contrast to the analogous unsubstituted tris(3-aminopyridinium) analogue, despite the fact that low-temperature (1)H NMR experiments reveal a total of four acetate-binding conformations. Photodimerization of anthracene units results in the formation of potential fluorescent anion sensors.     

Ultra low head–disk spacing measurement using dual beam polarisation interferometry

In this paper, a dual-beam normal incidence polarisation interferometer is proposed to measure the flying height or head–disk spacing. Using this interferometer, the head–disk spacing can be measured both in magnetic real disk condition and in glass disk condition. It has the advantage of both the currently popular intensity interferometry method and the oblique incidence polarisation interferometry method. With this polarisation interferometer, not only the flying height can be measured down to contact without losing accuracy, but the pitch and roll of the head-slider can also be detected dynamically. The optical parameters of the head-slider can also be determined. Design details and experimental study are presented.     

The determination of atmospheric concentrations of the active ingredients of pesticide formulations by high-performance liquid chromatography

Summary Methods of sampling atmospheres contaminated by pesticides in factory and agricultural environments, and subsequent analysis by HPLC, are discussed. Air sampling is carried out using porous polymer or filter collection media, usually a 100 dm³ air volume is suitable. Detection limits with ultra-violet detection are in the range 0.1 to 10 g m^–3.Presented at the 14th International Symposium on Chromatography London, September, 1982     

Application of the Schulze–Hardy rule to haematite and haematite/humate colloid stability

The applicability of the Schulze–Hardy rule to haematite and haematite/humate mixtures has been investigated by measuring the rate of fast and slow coagulation after the addition of increasing concentrations of mono, di and trivalent ions. Haematite colloids follow the rule for mono, di and trivalent ions. Haematite colloids coated with humate generally follow the rule for mono and di valent ions with the exception of copper ions. Trivalent ions do not follow the Schulze–Hardy rule because of their relatively strong complexation with humate. The size of the counter ion has an effect on the de-stabilising ability of ions of the same charge.     

On Circulant Complex Hadamard Matrices

We show that a circulant complex Hadamard matrix of order n is equivalent to a relative difference set in the group C ₄×C _n where the forbidden subgroup is the unique subgroup of order two which is contained in the C ₄ component. We obtain non-existence results for these relative difference sets. Our results are sufficient to prove there are no circulant complex Hadamard matrices for many orders.