Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Influence of unit operations on the levels of polyacetylenes in minimally processed carrots and parsnips: An industrial trial

Carrots and parsnips are often consumed as minimally processed ready-to-eat convenient foods and contain in minor quantities, bioactive aliphatic C17-polyacetylenes (falcarinol, falcarindiol, falcarindiol-3-acetate). Their retention during minimal processing in an industrial trial was evaluated. Carrot and parsnips were prepared in four different forms (disc cutting, baton cutting, cubing and shredding) and samples were taken in every point of their processing line. The unit operations were: peeling, cutting and washing with chlorinated water and also retention during 7 days storage was evaluated. The results showed that the initial unit operations (mainly peeling) influence the polyacetylene retention. This was attributed to the high polyacetylene content of their peels. In most cases, when washing was performed after cutting, less retention was observed possibly due to leakage during tissue damage occurred in the cutting step. The relatively high retention during storage indicates high plant matrix stability. Comparing the behaviour of polyacetylenes in the two vegetables during storage, the results showed that they were slightly more retained in parsnips than in carrots. Unit operations and especially abrasive peeling might need further optimisation to make them gentler and minimise bioactive losses.

The effect of construction pattern and unit interlock on the structural behaviour of block pavements

The maintenance or even replacement of cracked pavements requires considerable financial resources and puts a large burden on the budgets of local councils. In addition to these costs, local councils also face liability claims arising from uneven or cracked pedestrian pavements. These currently cost the Manchester City Council and Preston City Council around £6 million a year each. Design procedures are empirical. A better understanding of the interaction between paving blocks, bedding sand and subbase was necessary in order to determine the mode of failure of pavements under load. Increasing applied stress was found to mobilise ‘‘rotational interlock’’, providing increased pavement stiffness and thus increased load dissipation resulting in lower transmitted stress on the subgrade. The indications from the literature
review were that pavements are designed to fail by excessive deformation and that paving blocks remained uncracked at failure. This was confirmed with experimental data which was obtained from tests on segments of pavements that were laid/constructed in a purpose built test frame in the laboratory.

New light on death in prehistoric Malta: the Brochtorff Circle.

Trump, D., Malone, C and Stoddart, S., ,G. Burenhult, (ed.). 1993, Harper Collins: New York. p. 100-101.

An evaluation of protocolised weaning on the duration of mechanical ventilation

Using a before and after study design, we compared protocolised weaning from mechanical ventilation with usual non-protocolised practice in intensive care. Outcomes (duration of mechanical ventilation, duration of intubation, intensive care stay) and complications (re-intubations, tracheostomy, mortality) were compared between baseline (Phase I) and following implementation of protocolised weaning (Phase II). Over the same period, we collected data in a second (reference) unit to monitor practice changes over time. In the intervention unit, outcomes were longer in Phase II compared with Phase I (all p < 0.005). When adjusted for admission APACHE II score and diagnostic category, only intensive care stay remained significantly longer (p = 0.002). There were significantly more tracheostomies in Phase II (p = 0.004). The reference unit demonstrated no statistically significant differences in study outcomes or complications between Phases. Protocolised weaning did not reduce the duration of mechanical ventilation and was not associated with an increased rate of re-intubation or intensive care unit mortality.

Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

On the Uncoded BER Performance Bound of the IEEE 802.16d Channel

In this letter, the performance bound of the IEEE 802.16d channel is examined analytically in order to gain an insight into its theoretical potential. Different design strategies, such as orthogonal frequency division multiplexing (OFDM) and single-carrier frequency-domain equalization (SC-FDE), time-domain decision feedback equalization (DFE), and sphere decoder (SD) techniques are discussed and compared to the theoretical bound.

On the Problems of Mixing RCTs with Qualitative Research: The Case of the MRC Framework for the Evaluation of Complex Healthcare Interventions

In the perceived hierarchy of research designs, the results from randomized controlled trials are considered to provide the highest level of evidence. Indeed these trials have been upheld as the gold standard in research. The benefits and limitations of the randomized controlled trial as a method of evaluating the effectiveness of healthcare interventions are presented. The article then examines the different levels of complexity within healthcare interventions and the problems this poses in determining effectiveness. In an effort to provide a solution to this problem, the Medical Research Council produced a framework to assist investigators to develop and evaluate complex healthcare interventions. The framework is described with reference to an example of implementing and evaluating protocols for weaning patients in the intensive care unit. The framework is critiqued on the basis that it involves an ambiguous or contradictory ontology, which fails to articulate the relationship between the positivism of randomized controlled trials with the relativism of qualitative approaches. It is concluded that the use of realist strategies in combination with randomized controlled trials provides the most coherent solution to this quandary

The death of massive stars - I. Observational constraints on the progenitors of Type II-P supernovae

We present the results of a 10.5-yr, volume-limited (28-Mpc) search for supernova (SN) progenitor stars. In doing so we compile all SNe discovered within this volume (132, of which 27 per cent are Type Ia) and determine the relative rates of each subtype from literature studies. The core-collapse SNe break down into 59 per cent II-P and 29 per cent Ib/c, with the remainder being IIb (5 per cent), IIn (4 per cent) and II-L (3 per cent). There have been 20 II-P SNe with high-quality optical or near-infrared pre-explosion images that allow a meaningful search for the progenitor stars. In five cases they are clearly red supergiants, one case is unconstrained, two fall on compact coeval star clusters and the other twelve have no progenitor detected. We review and update all the available data for the host galaxies and SN environments (distance, metallicity and extinction) and determine masses and upper mass estimates for these 20 progenitor stars using the STARS stellar evolutionary code and a single consistent homogeneous method. A maximum likelihood calculation suggests that the minimum stellar mass for a Type II-P to form is m(min) = 8.5(-1.5)(+1) M-circle dot and the maximum mass for II-P progenitors is m(max) = 16.5 +/- 1.5 M-circle dot, assuming a Salpeter initial mass function holds for the progenitor population (in the range Gamma = -1.35(-0.7)(+0.3)). The minimum mass is consistent with current estimates for the upper limit to white dwarf progenitor masses, but the maximum mass does not appear consistent with massive star populations in Local Group galaxies. Red supergiants in the Local Group have masses up to 25 M-circle dot and the minimum mass to produce a Wolf-Rayet star in single star evolution (between solar and LMC metallicity) is similarly 25-30 M-circle dot. The reason we have not detected any high-mass red supergiant progenitors above 17 M-circle dot is unclear, but we estimate that it is statistically significant at 2.4 sigma confidence. Two simple reasons for this could be that we have systematically underestimated the progenitor masses due to dust extinction or that stars between 17-25 M-circle dot produce other kinds of SNe which are not II-P. We discuss these possibilities and find that neither provides a satisfactory solution. We term this discrepancy the 'red supergiant problem' and speculate that these stars could have core masses high enough to form black holes and SNe which are too faint to have been detected. We compare the Ni-56 masses ejected in the SNe to the progenitor mass estimates and find that low-luminosity SNe with low Ni-56 production are most likely to arise from explosions of low-mass progenitors near the mass threshold that can produce a core-collapse.

Fast automatic two-stage nonlinear model identification based on the extreme learning machine

It is convenient and effective to solve nonlinear problems with a model that has a linear-in-the-parameters (LITP) structure. However, the nonlinear parameters (e.g. the width of Gaussian function) of each model term needs to be pre-determined either from expert experience or through exhaustive search. An alternative approach is to optimize them by a gradient-based technique (e.g. Newton’s method). Unfortunately, all of these methods still need a lot of computations. Recently, the extreme learning machine (ELM) has shown its advantages in terms of fast learning from data, but the sparsity of the constructed model cannot be guaranteed. This paper proposes a novel algorithm for automatic construction of a nonlinear system model based on the extreme learning machine. This is achieved by effectively integrating the ELM and leave-one-out (LOO) cross validation with our two-stage stepwise construction procedure [1]. The main objective is to improve the compactness and generalization capability of the model constructed by the ELM method. Numerical analysis shows that the proposed algorithm only involves about half of the computation of orthogonal least squares (OLS) based method. Simulation examples are included to confirm the efficacy and superiority of the proposed technique.

On the nature of the progenitors of three Type II-P supernovae: 2004et, 2006my and 2006ov

The pre-explosion observations of the Type II-P supernovae 2006my, 2006ov and 2004et are re-analysed. In the cases of supernovae 2006my and 2006ov we argue that the published candidate progenitors are not coincident with their respective supernova sites in pre-explosion Hubble Space Telescope observations. We therefore derive upper luminosity and mass limits for the unseen progenitors of both these supernovae, assuming they are red supergiants: 2006my (log L/L-circle dot = 4.51; m

ON THE PROGENITOR AND EARLY EVOLUTION OF THE TYPE II SUPERNOVA 2009kr

We identify a source coincident with SN 2009kr in Hubble Space Telescope pre-explosion images. The object appears to be a single point source with an intrinsic color V - I = 1.1 +/- 0.25 and M-V = -7.6 +/- 0.6. If this is a single star, it would be a yellow supergiant of log L/L-circle dot similar to 5.1 and a mass of 15(-4)(+5) M-circle dot. The spatial resolution does not allow us yet to definitively determine if the progenitor object is a single star, a binary system, or a compact cluster. We show that the early light curve is similar to a Type IIL SN, but the prominent H alpha P-Cygni profiles and the signature of the end of a recombination phase are reminiscent of a Type IIP. The evolution of the expanding ejecta will play an important role in understanding the progenitor object.