Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Joined-up archaeology at Old Scatness, Shetland: thin section analysis of the site and hinterland

Excavations on the multi-period settlement at Old Scatness, Shetland have uncovered a number of Iron Age structures with compacted, floor-like layers. Thin section analysis was undertaken in order to investigate and compare the characteristics of these layers. The investigation also draws on earlier analyses of the Iron Age agricultural soil around the settlement and the midden deposits that accumulated within the settlement, to create a 'joined-up' analysis which considers the way material from the settlement was used and then recycled as fertiliser for the fields. Peat was collected from the nearby uplands and was used for fuel and possibly also for flooring. It is suggested that organic-rich floors from the structures were periodically removed and the material was spread onto the fields as fertilisers. More organic-rich material may have been used selectively for fertiliser, while the less organic peat ash was allowed to accumulate in middens. Several of the structures may have functioned as byres, which suggests a prehistoric plaggen system.

Phylogeny, biogeography, and ecology of Ficus section Malvanthera (Moraceae)

We conducted the first molecular phylogenetic study of Ficus section Malvanthera (Moraceae; subgenus Urostigma) based on 32 Malvanthera accessions and seven outgroups representing other sections of Ficus subgenus Urostigma. We used DNA sequences from the nuclear ribosomal internal and external transcribed spacers (ITS and ETS), and the glyceraldehyde-3-phosphate dehydrogenase (G3pdh) region. Phylogenetic analysis using maximum parsimony, maximum likelihood and Bayesian methods recovered a monophyletic section Malvanthera to the exclusion of the rubber fig, Ficus elastica. The results of the phylogenetic analyses do not conform to any previously proposed taxonomic subdivision of the section and characters used for previous classification are homoplasious. Geographic distribution, however, is highly conserved and Melanesian Malvanthera are monophyletic. A new subdivision of section Malvanthera reflecting phylogenetic relationships is presented. Section Malvanthera likely diversified during a period of isolation in Australia and subsequently colonized New Guinea. Two Australian series are consistent with a pattern of dispersal out of rainforest habitat into drier habitats accompanied by a reduction in plant height during the transition from hemi-epiphytic trees to lithophytic trees and shrubs. In contradiction with a previous study of Pleistodontes phylogeny suggesting multiple changes in pollination behaviour, reconstruction of changes in pollination behaviour on Malvanthera, suggests only one or a few gains of active pollination within the section. (C) 2008 Elsevier Inc. All rights reserved.

Morpholinone mediated oxazolone-free C-terminus amide coupling permitting a convergent strategy for peptide synthesis

3-Substituted-5-phenylmorpholinones have been demonstrated to act as N-protected C-terminus activated alpha-amino acids capable of undergoing solution phase N-terminus peptide extension following standard coupling procedures. The N-acylated morpholinones do not undergo epimerisation of the stereocentre of the C-terminus amino acid residue as oxazolone formation is sterically prevented, although C-terminus peptide coupling is still possible. This convergent approach to peptide synthesis is exemplified by the preparation of L-ala-L-ala-L-ala and L-ala-D-ala-L-ala. Copyright (c) 2008 European Peptide Society and John Wiley & Sons, Ltd.

An extension of the well-known quaternary section at Godrevy, St Ives Bay, West Cornwall: analysis and review

The well-known Quaternary section at Godrevy, west Cornwall has been often described during the past half century, however, a further section, about a kilometre to the south is considered for the first time since a brief mention at the beginning of the last century. This 200m long exposure rests upon a raised shore platform and consists of a basal raised beach and littoral sand, overlain by a local diamict revealing evidence of post-depositional frost disturbance and finally Holocene dune sand. It is proposed that this Strap Rock site be included within the general discussion of the Godrevy section.

Face verification using Gabor wavelets and AdaBoost

This paper presents a new face verification algorithm based on Gabor wavelets and AdaBoost. In the algorithm, faces are represented by Gabor wavelet features generated by Gabor wavelet transform. Gabor wavelets with 5 scales and 8 orientations are chosen to form a family of Gabor wavelets. By convolving face images with these 40 Gabor wavelets, the original images are transformed into magnitude response images of Gabor wavelet features. The AdaBoost algorithm selects a small set of significant features from the pool of the Gabor wavelet features. Each feature is the basis for a weak classifier which is trained with face images taken from the XM2VTS database. The feature with the lowest classification error is selected in each iteration of the AdaBoost operation. We also address issues regarding computational costs in feature selection with AdaBoost. A support vector machine (SVM) is trained with examples of 20 features, and the results have shown a low false positive rate and a low classification error rate in face verification.