Updating the (Supermassive Black Hole Mass) - (Spiral Arm Pitch Angle) Relation: A Strong Correlation for Galaxies with Pseudobulges

We have conducted an image analysis of the (current) full sample of 44 spiral galaxies with directly measured supermassive black hole (SMBH) masses, $M_{\rm BH}$, to determine each galaxy's logarithmic spiral arm pitch angle, $\phi$. For predicting black hole masses, we have derived the relation: $\log({M_{\rm BH}/{\rm M_{\odot}}}) = (7.01\pm0.07) - (0.171\pm0.017)[|\phi|-15\deg]$. The total root mean square scatter associated with this relation is 0.43 dex in the $\log{M_{\rm BH}}$ direction, with an intrinsic scatter of $0.33\pm0.08$ dex. The $M_{\rm BH}$-$\phi$ relation is therefore at least as accurate at predicting SMBH masses in spiral galaxies as the other known relations. By definition, the existence of an $M_{\rm BH}$-$\phi$ relation demands that the SMBH mass must correlate with the galaxy discs in some manner. Moreover, with the majority of our sample (37 of 44) classified in the literature as having a pseudobulge morphology, we additionally reveal that the SMBH mass correlates with the large-scale spiral pattern and thus the discs of galaxies hosting pseudobulges. Furthermore, given that the $M_{\rm BH}$-$\phi$ relation is capable of estimating black hole masses in bulge-less spiral galaxies, it therefore has great promise for predicting which galaxies may harbour intermediate-mass black holes (IMBHs, $M_{\rm BH}<10^5$ ${\rm M_{\odot}}$). Extrapolating from the current relation, we predict that galaxies with $|\phi| \geq 26.7\deg$ should possess IMBHs.Comment: 18 pages, 9 figures, and 4 tables. Accepted July 13. Received 2017 July 13; in original form 2017 May 2

Trade in mineral resources

This paper provides a review of current thinking on the economics of international trade in mineral resources. I first define what is meant by trade in mineral resources. I then discuss patterns of trade in mineral resources. The paper then moves on to the five topics requested by the World Trade Organization: theoretical and empirical literature on international trade in minerals; trade impacts of mineral abundance and the resource curse; the political economy of mineral trade in resource-abundant states; non-economic considerations associated with strategic mineral resources; and the impact of domestic market structure and regulation on production and trade in minerals

Comparing men's and womens' experiences of multiple exclusion homelessness

This article explores gender as a variable in multiple exclusion homelessness in England. Much past research has taken insufficient account of the gender of homeless people, especially the predominance of men in the single homeless population and of women heading homeless households with dependent children. Drawing on qualitative data generated in a study of multiple exclusion homelessness in London and Nottingham, the article considers three ways in which gender may act as a homelessness variable: in people's susceptibility to homelessness, in their experiences of homelessness and in their encounters with accommodation services. By comparing the accounts of homeless men and women with complex support needs with evidence from staff working for support agencies, the overall aim of the article is to offer a critical examination of the gendered assumptions of homelessness policy and practice

Density Functional Studies of the Structure and Bonding of Nitrosyl Metalloporphyrin Complexes

Density functional calculations were used to determine optimized geometries fornitrosyl-metalloporphyrin complexes of Fe(II),Co(II)and Mn(II).The optimized structures were found to be consistent with experimental data and previous computational predictions using single point density functional calculations. Vibrational frequencies for the N-0stretching mode were also calculated and shown to be consistent with experimental data. The nature of the bonding between the metal center and nitrosyl ligand is discussed in relation to the structure of the M-N-0 linkage. The results were found to be consistent with previous descriptions derived from the Fenske-Hall approximate molecular orbital method. Other interesting structural features in the optimized geometries are noted

Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation

We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a {\em rotating} dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched through the critical point for condensation, as in the experiment of Haljan et al. [Phys. Rev. Lett., 87, 21043 (2001)]. In contrast to stirring a vortex-free condensate, where topological constraints require that vortices enter from the edge of the condensate, we find that phase defects in the initial non-condensed cloud are trapped en masse in the emerging condensate. Bose-stimulated condensate growth proceeds into a disordered vortex configuration. At sufficiently low temperature the vortices then order into a regular Abrikosov lattice in thermal equilibrium with the rotating cloud. We calculate the effect of thermal fluctuations on vortex ordering in the final gas at different temperatures, and find that the BEC transition is accompanied by lattice melting associated with diminishing long range correlations between vortices across the system.Comment: 15 pages, 12 figure