A new approach to reduction of the Neumann problem in acoustic scattering to a non-hypersingular integral equation

The Neumann problem for the propagative Helmholtz equation inthe exterior of several bodies (obstacles) is studied in twoand three dimensions by a special modification of the boundaryintegral equation method. This modification can be called the'method of interior boundaries', because additional boundariesare introduced inside scattering bodies. The solution of theproblem is obtained in the form of a single layer potentialon the whole boundary. The density in the potential satisfiesthe uniquely solvable Fredholm equation of the second kind andcan be computed by standard codes. In fact our method holdsfor any positive wave numbers.     

Topological regular variation: III. Regular variation

This paper extends the topological theory of regular variation of the slowly varying case of Bingham and Ostaszewski (2010) [5] to the regularly varying functions between metric groups, viewed as normed groups (see also Bingham and Ostaszewski (2010) [6]). This employs the language of topological dynamics, especially flows and cocycles. In particular we show that regularly varying functions obey the chain rule and in the non-commutative context we characterize pairs of regularly varying functions whose product is regularly varying. The latter requires the use of a ‘differential modulus’ akin to the modulus of Haar integration.     

Ratio Mercerian Theorems with Applications to Hankel and Fourier Transforms

We complete and complement our recent work on Drasin-Shea-Jordantheorems for Fourier and Hankel transforms. In improving onthe methods of our previous work, we were led to certain ratioMercerian theorems for general kernels; these yield definitiveversions of our earlier results for Fourier and Hankel transforms.1991 Mathematics Subject Classification: primary 44A15; secondary47B38.     

Quantification of isoflavones and lignans in serum using isotope dilution liquid chromatography/tandem mass spectrometry

Phytoestrogens (isoflavones and lignans) are receiving increasing attention due to a potential protective effect against a number of complex diseases. However, in order to investigate these associations, it is necessary to accurately quantify the levels of phytoestrogens in foods and biological fluids. We report an assay for three isoflavones (daidzein, genistein, and glycitein), two metabolites of daidzein (O-desmethylangolensin and equol), and two lignans (enterodiol and enterolactone) in human serum using electrospray ionisation liquid chromatography/mass spectrometry (LC/MS) with selective reaction monitoring. A simple, highly automated sample preparation procedure requires only 200 microL of sample and utilises one solid-phase extraction stage. Limits of detection are in the region of 10 pg/mL for all analytes except equol, which had a limit of detection of approximately 100 pg/mL. The method developed is suitable for measuring the concentrations of phytoestrogens in blood samples collected from large epidemiological studies. The results of the analysis of serum samples from 300 men and women living in the UK are reported.     

Site-Directed Mutagenesis and Analysis of Second-Site Revertants Indicates a Requirement for C-Terminal Amino Acids of PsaB for Stable Assembly of the Photosystem I Reaction Center Complex in Chlamydomonas reinhardtii

The PsaA and PsaB polypeptides form the reaction center core heterodimer of photosystem I (PSI). Both PsaA and PsaB are predicted to have 11 hydrophobic domains, although it is unclear how both polypeptides fold within the thylakoid membrane. If all 11 hydrophobic regions form membrane-spanning domains, the N- and C-terminus must be located on opposite sides of the membrane. The C-terminus of PsaB is very conserved in a wide range of organisms and may be important for PSI assembly or function. Using chloroplast transformation in Chlamydomonas reinhardtii we have generated a series of C-terminal extension and deletion mutants of the PsaB polypeptide. Analysis of these mutants and spontaneous revertants indicates that the C-terminus may be extended by at least 14 amino acids without impairing PSI assembly. Deletion of amino acids 732–736 also has no impact on PSI, whereas deletion of amino acids 727–736 results in no accumulation of the complex. The site of truncation in the 727–736 deletion coincides with the end of the hydrophobic domain XI supporting a location of the C-terminus of PsaB on the lumenal side of PSI.     

Polymerization of aromation amines with ferric chloride to produce thermally stable polymers

Simple aromatic amines have been polymerized by use of ferric chloride as a combined Friedel-Crafts catalyst and oxidant to yield polymers which are both thermally and oxidatively stable. Under certain reaction conditions a polydiphenylamine was prepared which was stable in air up to 465°C as shown by thermogravimetric analysis. This polymer has a softening point of ca. 80–100°C and is soluble in some organic solvents. Such a polydiphenylamine and other polymers with similar properties are regarded as useful for conversion to thermally stable Phillips-type resins by crosslinking with conventional difunctional agents.     

Polymorph VI of sulfapyridine: interpenetrating two‐ and three‐dimensional hydrogen‐bonded nets formed from two tautomeric forms

Polymorph VI of 4‐amino‐N‐(2‐pyridyl)benzenesulfonamide, C₁₁H₁₁N₃O₂S, is monoclinic (space group P2₁/n). The asymmetric unit contains two different tautomeric forms. The structure displays N—H...N and N—H...O hydrogen bonding. The two independent molecules form two separate two‐ and three‐dimensional hydrogen‐bonded networks which interpenetrate. The observed patterns of hydrogen bonding are analogous to those in polymorph I of sulfathiazole.     

Mössbauer studies of phosphate glasses for the immobilisation of toxic and nuclear wastes

Various iron-containing phosphate glasses were investigated by Mössbauer spectroscopy. Iron was found to occur predominantly as Fe³⁺ in all glasses, and largely occupied sites with distorted octahedral coordination for both redox states. Using a base glass of nominal composition 60 P₂O₅–40 Fe₂O₃ (mol%), stepwise molar replacement of Fe₂O₃ by (0.67 Na₂O?×?0.33 Al₂O₃) increased the redox ratio, Fe²⁺/ΣFe, from 0.13 at 40% Fe₂O₃ to 0.25 at 10% Fe₂O₃. The centre shift increased and quadrupole splitting decreased by up to ～20% over this range, interpreted as a decrease in the average distortion of Fe sites from cubic symmetry, and an increase in average iron coordination. Literature revealed that recoil-free fraction ratio f (Fe³⁺)?/?f (Fe²⁺)?≈?1.3 in iron phosphate glasses, and this was considered when assessing redox. Mössbauer parameters of these and other glasses demonstrated a combination of structural stability and compositional flexibility which makes them so suitable for waste immobilisation.     

A kinetic approach to Bose-Einstein condensates: Self-phase modulation and Bogoliubov oscillations

A kinetic approach to Bose-Einstein condensates (BECs) is proposed based on the Wigner-Moyal equation (WME). In the semiclassical limit, the WME reduces to the particle-number conservation equation. Two examples of applications are (i) a self-phase modulation of a BE condensate beam, where we show that part of the beam is decelerated and eventually stops as a result of the gradient of the effective self-potential, and (ii) the derivation of a kinetic dispersion relation for sound waves in BECs, including collisionless Landau damping.