Singly generated planar algebras of small dimension, Part II

We classified in Bisch and Jones (Duke Math. J. 101 (2000) 41) all spherical C∗-planar algebras generated by a non-trivial 2-box subject to the condition that the dimension of N′∩M₂ is ?12. We showed that they are given by the Fuss-Catalan systems discovered in Bisch and Jones (Invent. Math. 128 (1997) 89) and one exceptional planar algebra. In the present paper, we extend these results and show that there is only one spherical C∗-planar algebra generated by a single non-trivial 2-box if the dimension of N′∩M₂ is 13. It is given by the standard invariant of the crossed product subfactor , where D₅ denotes the dihedral group with 10 elements.     

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Radio Echo Sounding of Pine Island Glacier, West Antarctica: Aperture Synthesis Processing and Analysis of Feasibility From Space

Airborne radio echo sounding of the West Antarctic Ice Sheet over Pine Island Glacier was performed in the austral summer of 2004/2005 under the National Science Foundation's West Antarctic Ice Sheet Initiative. The British Antarctic Survey flew its newly developed 150-MHz ice-sounding radar over Pine Island Glacier and collected approximately 35 000 km of sounding data. The synthetic aperture radar (SAR) technique was applied to process those data in order to enhance radar signatures from the bed. As a matter of fact, airborne ice-sounding radar systems are generally affected by surface clutter returns, masking the echoes of internal layers and ice-bedrock transition at a large depth. Focused and unfocused (Doppler filtering) SAR techniques were compared, and their respective advantages/disadvantages were analyzed. Enhancement of bedrock detection at a large depth (> 2000 m) through SAR processing is demonstrated. Finally, a simulation analysis was performed for assessing the feasibility of ice-sheet sounding from space. It is shown that the gain in bed detection threshold is marginal in the satellite sounding geometry. Airborne radar, Antarctica, ice sounding, satellite remote sensing, subglacial topography, synthetic aperture radar (SAR) processing, West Antarctic Ice Sheet.     

Diversity gain from a single-port adaptive antenna using switchedparasitic elements illustrated with a wire and monopole prototype

A new concept in single-port adaptive antennas using parasitic elements with switched terminating impedances is presented including results from a concept prototype. Each parasitic element can be effectively terminated in three impedance values. The antenna concept provides multiple radiation patterns with a single RF signal port without the need for RF switches or phase shifters in the direct RF signal path. Impedance variations in the active antenna element are minimized by use of only rotationally symmetric configurations. Measured patterns are used to demonstrate the performance improvement expected using switched diversity combining in a simulated uniform scattering scenario. The concept prototype having one active element and four parasitic elements, is shown to have equivalent diversity performance to between three and four uncorrelated branches     

Bacterial growth response to photoactive quinones

Quinones are known producers of reactive oxygen species (ROS) that may be toxic in natural aquatic environments. In this study, the effects of parent quinones and their photodegradation products on bacterial growth were determined, and photochemical ROS formation rates were measured. Using (3)H-leucine incorporation to measure growth of the bacterium Pseudomonas aeruginosa and natural seawater bacterioplankton, growth inhibition was observed when samples were exposed to dichlone, chloranil and sodium anthraquinone-2-sulfonate (AQ2S). For seawater, compared with other quinones tested, dichlone showed the greatest toxicity in the dark, and AQ2S toxicity was greatest during simultaneous exposure to sunlight. Photodegraded chloranil and dichlone showed decreased toxicity compared with nonirradiated samples. For P. aeruginosa, AQ2S and its photodegradation products showed the greatest toxicity during simultaneous exposure to sunlight. Chloranil photodegradation products showed reduced toxicity compared with the parent compound during simultaneous exposure to sunlight. Dichlone was the only compound to show any toxicity to P. aeruginosa in the dark, and its photodegradation products were more toxic than the parent compound. Based on the results of dark and light controlled experiments measuring bacterial growth and estimated ROS production rates, ROS alone does not account for relative differences in toxicity between these quinones.     

On optical depth profiling using confocal Raman spectroscopy

Until 2006 the performance of confocal Raman spectroscopy depth profiling was typically described and modeled through the application of geometrical optics, including refraction at the surface, to explain the degree of resolution and the precise form of the depth profile obtained from transparent and semicrystalline materials. Consequently a range of techniques, physical and analytical, was suggested to avoid the errors thus encountered in order to improve the practice of Raman spectroscopy, if not the understanding of the underlying mechanisms. These approaches were completely unsuccessful in accounting for the precise form of the depth profile, the fact that spectra obtained from laminated samples always contain characteristic peaks from all materials present both well above and below the focal point and that spectra can be obtained when focused some 40 μm above the sample surface. This paper provides further evidence that the physical processes underlying Raman spectroscopy are better modeled and explained through the concept of an extended illuminated volume contributing to the final Raman spectrum and modeled through a photon scattering approach rather than a point focus ray optics approach. The power of this numerical model lies in its ability to incorporate, simultaneously, the effects of degree of refraction at the surface (whether using a dry or oil objective lens), the degree of attenuation due to scatter by the bulk of the material, the Raman scattering efficiency of the material, and surface roughness effects. Through this we are now able to explain why even removing surface aberration and refraction effects through the use of oil immersion objective lenses cannot reliably ensure that the material sampled is only that at or close to the point of focus of the laser. Furthermore we show that the precise form of the depth profile is affected by the degree of flatness of the surface of the sample. Perhaps surprisingly, we show that the degree of flatness of the material surface is, in fact, more important than obtaining a precise refractive index match between the immersion oil and the material when seeking a high-quality depth profile or Raman spectrum from within a transparent or semicrystalline material, contrary to accepted norms that samples for interrogation by Raman spectroscopy require little preparation.     

The general Goldbach problem with Beatty primes

In this paper, we are concerned with the representation of large positive integers as the sum of a fixed number of prime numbers taken from Beatty sequences. We are able to avoid any conditions on the Beatty sequences that they be of finite type which have been required hitherto. We use a form of the Hardy–Littlewood–Vinogradov method, but the proofs are quite delicate.