Spectral properties of non-local uniformly-elliptic operators

In this paper we consider the spectral properties of a class of non-local uniformly elliptic operators, which arise from the study of non-local uniformly elliptic partial differential equations. Such equations arise naturally in the study of a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics. The operators studied here are bounded perturbations of linear (local) differential operators, and the non-local perturbation is in the form of an integral term. We study the eigenvalues, the multiplicities of these eigenvalues, and the existence of corresponding positive eigenfunctions. It is shown here that the spectral properties of these non-local operators can differ considerably from those of their local counterpart. However, we show that under suitable hypotheses, there still exists a principal eigenvalue of these operators

Reconstructing the linear power spectrum of cosmological mass fluctuations

We describe an attempt to reconstruct the initial conditions for the formation of cosmological large-scale structure. The power spectrum of the primordial fluctuations is affected by bias, nonlinear evolution and redshift-space distortions, but we show how these effects can be corrected for analytically. Using eight independent datasets, we obtain excellent agreement in the estimated linear power spectra given the following conditions. First, the relative bias factors for Abell clusters, radio galaxies, optical galaxies and IRAS galaxies must be in the ratios 4.5:1.9:1.3:1. Second, the data require redshift-space distortion: \Omega^{0.6}/b_{\ss I} = 1.0 \pm 0.2. Third, low values of $\Omega$ and bias are disfavoured. The shape of the spectrum is extremely well described by a CDM transfer function with an apparent value of the fitting parameter $\Omega h =0.25$. Tilted models predict too little power at 100 Mpc wavelengths.Comment: Edinburgh Astronomy Preprint 26/93. Accepted for publication in Monthly Notices of the RAS. 13 pages of LaTeX, plus 10 PostScript figures. You will need the mn.sty style file (from babbage: get mn.sty). The figure .ps files are in the usual self-unpacking unix scrip

Dust emission in powder handling: Free falling particle plume characterisation

Dust generation during solids handling, principally from the free falling of bulk materials and their impact on stockpiles, can be a health threat for operators and a cause of dust explosions. The proper design of a dust emission control system requires knowledge of the behaviour of the free falling jet, in particular the amount of air entrained by the falling powder and the concentration of dust liberated. The focus in this present paper is on the effect of drop height of a free falling jet on segregation by particle size, particle velocity, changes in particle concentration and entrained air in the dust plume. This gives a quantification of the important parameters and the concentration of dust emitted during a free fall

Granular flows down inclined channels with a strain-rate dependent friction coefficient. Part I: Non-cohesive materials

The flow of a granular material down an incline of finite width with a strain-rate dependent coefficient of friction and a conical yield criterion is semi-analytically obtained using a characteristic method for flows on a deep layer of grains. This analysis leads to a flow field with three distinct zones: a Bagnold-flow zone below the free surface, a dead zone and a matching zone between the two, linked to slippage at the wall. A good agreement between the computed flow field and experimental data is obtained

N-heterocyclic germylenes: structural characterisation of some heavy analogues of the ubiquitous N-heterocyclic carbenes

The X-ray crystal structures of three N-heterocyclic germylenes (NHGes) have been elucidated including the previously unknown 1,3-bis(2,6-dimethylphenyl)diazagermol-2-ylidene (1). In addition, the X-ray crystal structures of the previously synthesised 1,3-bis(2,4,6-trimethylphenyl)diazagermol-2-ylidene (2) and 1,3-bis(2,6-diisopropylphenyl)diazagermol-2-ylidene (3) are also reported. The discrete molecular structures of compounds 1 to 3 are comparable, with Ge-N bond lengths in the range 1.835-1.875 Å, while the N-Ge-N bond angles range between 83.6 and 85.2°. Compound 2 was compared to the analogous N-heterocyclic carbene species, 1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene (IMes). The major geometrical difference observed, as expected, was the bond angle around the divalent group 14 atom. The N-Ge-N bond angle was 83.6° for compound 2 versus the N-C-N bond angle of 101.4° for IMes. The Sn equivalent of (1), 1,3-bis(2,6-dimethylphenyl)diazastannol-2-ylidene (4), has also been synthesised and its crystal structure is reported here. In order to test their suitability as ligands, compounds 1 to 3 were reacted with a wide range of transition metal complexes. No NHGes containing metal complexes were observed. In all cases the NHGe either degraded or gave no reaction

Families 'at risk' and the family nurse partnership:the intrusion of risk into social exclusion policy

This article considers why the family nurse partnership (FNP) has been promoted as a means of tackling social exclusion in the UK. The FNP consists in a programme of visits by nurses to low-income first-time mothers, both while the mothers are pregnant and for the first two years following birth. The FNP is focused on both teaching parenthood and encouraging mothers back into education and/or into employment. Although the FNP marks a considerable discontinuity with previous approaches to family health, it is congruent with an emerging new approach to social exclusion. This new approach maintains that the most important task of social policy is to identify quickly the most 'at-risk' households, individuals and children so that interventions can be targeted more effectively at those 'at risk', either to themselves or to others. The article illustrates this new approach by analysing a succession of reports by the Social Exclusion Unit. It indicates that there is a considerable amount of ambiguity about the relationship between specific risk-factors and being 'at risk of social exclusion'. Nonetheless, this new approach helps to explain why British policy-makers may have chosen to promote the new FNP now

Families 'at risk' and the family nurse partnership:the intrusion of risk into social exclusion policy

This article considers why the family nurse partnership (FNP) has been promoted as a means of tackling social exclusion in the UK. The FNP consists in a programme of visits by nurses to low-income first-time mothers, both while the mothers are pregnant and for the first two years following birth. The FNP is focused on both teaching parenthood and encouraging mothers back into education and/or into employment. Although the FNP marks a considerable discontinuity with previous approaches to family health, it is congruent with an emerging new approach to social exclusion. This new approach maintains that the most important task of social policy is to identify quickly the most 'at-risk' households, individuals and children so that interventions can be targeted more effectively at those 'at risk', either to themselves or to others. The article illustrates this new approach by analysing a succession of reports by the Social Exclusion Unit. It indicates that there is a considerable amount of ambiguity about the relationship between specific risk-factors and being 'at risk of social exclusion'. Nonetheless, this new approach helps to explain why British policy-makers may have chosen to promote the new FNP now

Structural and metabolic studies on normal and pathological bone

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Bone is refractory to most conventional biochemical Procedures. However because it is now possible to cut sections (e. g. lopm) of fresh, undemineralized adult bone, this tissue can be analyzed by suitably modified methods of quantitative cytochemistry. A new substrate for assaying hydroxyacyl dehydrogenase activity demonstrated that bone cells may use fatty acids as a major source of energy: detailed analysis of the activities of key enzymes indicated that the paradox of ‘aerobic glycolysis’ of bone could be explained by fatty acid oxidation satisfying the requirements of the Krebs' cycle and directing the conversion of pyruvate to lactate The influence of glucose 6-phosphate dehydrogenase (G6PD) activity in aerobic glycolysis has been considered. The inverse relationships between this activity and that of Na-K-ATPase led to the development of a new method for the latter, based on a new concept in cytochemistry ('hidden-capture' procedure). A major feature of fracture-healing is increased periosteal G6PD activity. The association with the vitamin K cycle has been investigated by feeding rats with dicoumarol which not only inhibited bone-formation but also G6PD activity. The stimulation of this activity in fracture-healing has been linked with ornithine decarboxylase (ODC) activity, for which a new method has been developed. Rats deficient in pyridoxal phosphate (cofactor for ODC) had decreased G6PD responses and also appeared to become osteoporotic. Studies on osteoporotic fractures in the human showed the presence of relatively large apatite crystals close to the fracture-site, and disorganized glycosaminoglycans (demonstrated by the new method of ‘induced birefringence’)