Approximation in reflexive Banach spaces and applications to the invariant subspace problem

We formulate a general approximation problem involving reflexive and smooth Banach spaces, and give its explicit solution. Two applications are presented— the first is to the Bounded Completion Problem involving approximation of Hardy class functions, while the second involves the construction of minimal vec- tors and hyperinvariant subspaces of linear operators, generalizing the Hilbert space technique of Ansari and Enflo

Approximation in reflexive Banach spaces and applications to the invariant subspace problem

We formulate a general approximation problem involving reflexive and smooth Banach spaces, and give its explicit solution. Two applications are presented— the first is to the Bounded Completion Problem involving approximation of Hardy class functions, while the second involves the construction of minimal vec- tors and hyperinvariant subspaces of linear operators, generalizing the Hilbert space technique of Ansari and Enflo

Shame and self-acceptance in continued flux: qualitative study of the embodied experience of significant weight loss and removal of resultant excess skin by plastic surgery

This study explored the embodied experience of body change using a qualitative design. Eight previous plastic surgery patients of a London hospital took part in in-depth, semi-structured interviews 1 year post a plastic surgery procedure to remove excess skin around their abdomen, resulting from weight loss. Participant interviews were analysed using Interpretative Phenomenological Analysis. Two sub-themes titled 'Shame of the hidden body' and 'Lack of acceptance; the future focused body' are presented in this article. Findings are considered in relation to theories of 'Body Shame' and in the current cultural context

In situ analysis of pH gradients in mosquito larvae using non-invasive, self-referencing, pH-sensitive microelectrodes

The alkaline environment, pH approximately 11, in the anterior midgut lumen of mosquito larvae is essential for normal nutrition and development. The mechanism of alkalization is, however, unknown. Although evidence from immunohistochemistry, electron microscopy and electrophysiology suggests that a V-ATPase is present in the basal membranes of the epithelial cells, its physiological role in the alkalization process has not been demonstrated. To investigate a possible role of the V-ATPase in lumen alkalization, pH gradients emanating from the hemolymph side of the midgut in semi-intact mosquito larvae were measured using non-invasive, self-referencing, ion-selective microelectrodes (SERIS). Large H+ concentration gradients, with highest concentrations close to the basal membrane (outward [H+] gradients), were found in the anterior midgut, whereas much smaller gradients, with concentrations lowest close to this membrane (inward [H+] gradients), were found in the gastric caeca and posterior midgut. Similar region-specific pH gradients, with consistent anterior-to-posterior profiles, were observed in individuals of two Aedes species, Aedes aegypti from semi-tropical Florida and Aedes canadensis from north-temperate Massachusetts. The gradients remained in a steady state for up to 6 h, the maximum duration of the recordings. Bafilomycin A1 (10(-5), 10(-7 )mol x l(-1)) on the hemolymph side greatly diminished the [H+] gradients in the anterior midgut but had no effect on the gradients in the gastric caecum and posterior midgut. These physiological data are consistent with the previous findings noted above. Together, they support the hypothesis that a basal, electrogenic H+ V-ATPase energizes luminal alkalization in the anterior midgut of larval mosquitoes

Lubricant degradation, transport and the effect of extended oil drain intervals on piston assembly tribology

There are ever increasing demands on lubricant manufacturers to meet governmental legislation and customer needs by improving fuel economy, engine durability and exhaust system compatibility as shown by the introduction of GF4 and move towards GF5 specification oils. This has created an ever increasing need to understand how oil degrades in an engine and how this degraded oil affects piston assembly tribology. This review conference paper will give an overview of a collaborative project that has been undertaken to further enhance the understanding of how lubricant degrades in an operating engine, its transport through the engine and effect upon piston assembly tribology

Extraction and tribological investigation of top piston ring zone oil from a gasoline engine

With tightening emission regulations, increased expected fuel economy, and longer drain intervals impacting on lubricant formulation, greater understanding of how oil degrades in an automotive engine is becoming ever more important. Equally significant is the effect that this degraded lubricant has on the tribological operation of the engine, particularly its overall internal friction and component wear. In a previous paper, four tests to degrade oil in a single cylinder engine were reported [1]. These tests were set up such that the lubricating oil was degraded in the ring pack before returning to the sump, where it was sampled and chemical and rheological analysis undertaken. This paper reports the extension of this work using the same Hydra engine and describes how oil has additionally been extracted from the rear of the top piston ring during engine operation. This extracted oil has then been subjected to similar analysis as the sump oil samples in the previous tests, along with additional analysis to look at the tribological properties of the oil using tribometers. The results clearly show significant differences in the rheological, tribological, and chemical properties of the fresh oil and used sump oil samples when compared with the top ring zone (TRZ) oil samples, particularly the effect of load on the levels of volatiles present in the TRZ samples and their effect on traction and friction coefficient values during tribological testing

The SINFONI Nearby Elliptical Lens Locator Survey: discovery of two new low-redshift strong lenses and implications for the initial mass function in giant early-type galaxies

We present results from a blind survey to identify strong gravitational lenses among the population of low-redshift early-type galaxies. The SINFONI Nearby Elliptical Lens Locator Survey (SNELLS) uses integral-field infrared spectroscopy to search for lensed emission line sources behind massive lens candidates at z 300 km s− 1) and α-element abundances ([Mg/Fe] > 0.3). From the lensing configurations we derive total J-band mass-to-light ratios of 1.8 ± 0.1, 2.1 ± 0.1 and 1.9 ± 0.2 within the ∼2 kpc Einstein radius. Correcting for estimated dark matter contributions, and comparing to stellar population models with a Milky Way (Kroupa) initial mass function (IMF), we determine the ‘mass excess factor’, α. Assuming the lens galaxies have ‘old’ stellar populations (10 ± 1 Gyr), the average IMF mass factor is 〈α〉 = 1.10 ± 0.08 ± 0.10, where the first error is random and the second is systematic. If we instead fit the stellar populations from 6dF optical survey spectra, all three galaxies are consistent with being old, but the age errors are 3–4 Gyr, due to limited signal-to-noise ratio. The IMF constraints are therefore looser in this case, with 〈α〉 = 1.23+0.16−0.13±0.10. Our results are thus consistent with a Kroupa IMF (α = 1.00) on average, and strongly reject very heavy IMFs with α ≳ 2. A Salpeter IMF (α = 1.55) is inconsistent at the 3.5σ level if the galaxies are old, but cannot be excluded using age constraints derived from the currently available optical spectra