A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Landscape evolution and ice-sheet behaviour in a semi-arid polar environment: James Ross Island, NE Antarctic Peninsula

This study of landscape evolution presents both new modern and palaeo process-landform data, and analyses the behaviour of the Antarctic Peninsula Ice Sheet through the Last Glacial Maximum (LGM), the Holocene and to the present day. Six sediment-landform assemblages are described and interpreted for Ulu Peninsula, James Ross Island, NE Antarctic Peninsula: (1) the Glacier Ice and Snow Assemblage; (2) the Glacigenic Assemblage, which relates to LGM sediments and comprises both erratic-poor and erratic-rich drift, deposited by cold-based and wet-based ice and ice streams respectively; (3) the Boulder Train Assemblage, deposited during a Mid-Holocene glacier readvance; (4) the Ice-cored Moraine Assemblage, found in front of small cirque glaciers; (5) the Paraglacial Assemblage including scree, pebble-boulder lags, and littoral and fluvial processes; and (6) the Periglacial Assemblage including rock glaciers, protalus ramparts, blockfields, solifluction lobes and extensive patterned ground. The interplay between glacial, paraglacial and periglacial processes in this semi-arid polar environment is important in understanding polygenetic landforms. Crucially, cold-based ice was capable of sediment and landform genesis and modification. This landsystem model can aid the interpretation of past environments, but also provides new data to aid the reconstruction of the last ice sheet to overrun James Ross Island.

Disorder-specific functional abnormalities during temporal discounting in youth with Attention Deficit Hyperactivity Disorder (ADHD), Autism and comorbid ADHD and Autism

Attention Deficit Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD) are often comorbid and share cognitive abnormalities in temporal foresight. A key question is whether shared cognitive phenotypes are based on common or different underlying pathophysiologies and whether comorbid patients have additive neurofunctional deficits, resemble one of the disorders or have a different pathophysiology. We compared age- and IQ-matched boys with non-comorbid ADHD (18), non-comorbid ASD (15), comorbid ADHD and ASD (13) and healthy controls (18) using functional magnetic resonance imaging (fMRI) during a temporal discounting task. Only the ASD and the comorbid groups discounted delayed rewards more steeply. The fMRI data showed both shared and disorder-specific abnormalities in the three groups relative to controls in their brain-behaviour associations. The comorbid group showed both unique and more severe brain-discounting associations than controls and the non-comorbid patient groups in temporal discounting areas of ventromedial and lateral prefrontal cortex, ventral striatum and anterior cingulate, suggesting that comorbidity is neither an endophenocopy of the two pure disorders nor an additive pathology.