Quantifying the Coexistence of Massive Black Holes and Dense Nuclear Star Clusters

In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a 10^6-10^9 M_Sun supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a 10^5-10^7 M_Sun nuclear star cluster. To date, few galaxies have been found with both type of nuclei coexisting and even less have had the masses determined for both central components. Here we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei - which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range from 10^8 to 10^11 M_Sun, we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few percent to ~0.3 percent such that log[(M_BH+M_NC)/M_sph] = -(0.39+/-0.07)log[M_sph/10^10 M_Sun] -(2.18+/-0.07). Once dry merging has commenced by M_sph ~ 10^11 M_Sun and the nuclear star clusters have disappeared, this ratio is expected to become a constant value. As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters can be well approximated with Sersic functions having a range of indices from ~0.5 to ~3, the latter index describing the Milky Way's nuclear star cluster.Comment: To appear in MNRA

Volume renormalization for complete Einstein--K\"ahler metrics

For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete K\"ahler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply the result to derive a renormalized Chern--Gauss--Bonnet formula. Relations between renormalized volume and the CR $Q$-curvature are also investigated.Comment: Minor corrections to the statements and proofs of the main theorem and corollary. Included the example of the Bergman metric on the ball. To appear in Differential Geometry and Its Application

On the number of unlabeled vertices in edge-friendly labelings of graphs

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}. We say an edge-friendly labeling induces a \emph{partial vertex labeling} if vertices which are incident to more edges labeled 1 than 0, are labeled 1, and vertices which are incident to more edges labeled 0 than 1, are labeled 0. Vertices that are incident to an equal number of edges of both labels we call \emph{unlabeled}. Call a procedure on a labeled graph a \emph{label switching algorithm} if it consists of pairwise switches of labels. Given an edge-friendly labeling of $K_n$, we show a label switching algorithm producing an edge-friendly relabeling of $K_n$ such that all the vertices are labeled. We call such a labeling \textit{opinionated}.Comment: 7 pages, accepted to Discrete Mathematics, special issue dedicated to Combinatorics 201

The New Silk Road and the Northern Distribution Network: A Golden Road to Central Asian Trade Reform?

The United States is promoting a "New Silk Road" that would link Afghanistan to Southern and Central Asia via an interconnected web of transit corridors, which could transform the regional trade environment, tear down commercial barriers, and offer economic benefits for all.The New Silk Road and the Northern Distribution Network is a constructive assessment of the conditions and challenges facing this effort that asks and answers the following questions: Is the Northern Distribution network incentivizing regional cooperation and border reforms?Is the Northern Distribution Network helping to fight corruption in Central Asia?Has the Northern Distribution Network made transhipment through Central Asia more efficient?Are ordinary Central Asian citizens benefitting from Northern Distribution Network trade?Downloa

Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions

We compute energies and energy densities of static electromagnetic flux tubes in three and four spacetime dimensions. Our calculation uses scattering data from the potential induced by the flux tube and imposes standard perturbative renormalization conditions. The calculation is exact to one-loop order, with no additional approximation adopted. We embed the flux tube in a configuration with zero total flux so that we can fully apply standard results from scattering theory. We find that upon choosing the same on-shell renormalization conditions, the functional dependence of the energy and energy density on the parameters of the flux tube is very similar for three and four spacetime dimensions. We compare our exact results to those obtained from the derivative and perturbation expansion approximations, and find good agreement for appropriate parameters of the flux tube. This remedies some puzzles in the prior literature.Comment: 49 pages, 13 figures, minor changes in wording, accepted for publication in Nucl. Phys.

Are We Living in a Simulation?

If we are living inside of a simulation, what’s wrong with that? Nick Bostrom, a swedish philosopher has proposed the question of whether we are living in a simulation. Philosophers in the past have grappled with this concept, from Plato to George Berkeley. In this thesis, I intend to argue or prove that we may be living inside of a simulation or to my best ability find some approximation to the truth of the matter

Bullying in a primary school : a case study

Bullying has become a significant issue for schools and one that has attracted the media spotlight. It has also received considerable attention from the research community since the late 1980s following the tradition established through the work of many Scandinavian researchers. Much of the research has been longitudinal and sought to illuminate the experience of children who bullied or were being bullied. There has been considerably less research into teachers' and parents' understanding and experience of bullying between school children. This thesis seeks to rectify that situation by examining the views of Year 5 and 6 pupils, teachers and a sample of parents from a case study primary school. The research was conducted over a period of two years in a school referred to under the pseudonym Nicholas Street. The thesis investigates three questions: first, the meaning that key parties attribute to the term bullying; second, the nature of their experience in the context of the school; and third, their views on how it is handled or resolved. Data were collected through semi-structured interviews and reinterviews with teachers; unstructured and semi-structured interviews, questionnaires and a selection 'game' with pupils and semi-structured interviews and questionnaires with parents. All interviews were audio-taped and transcribed onto a computer database (Hyperqual) and questionnaire responses from pupils were analysed with the support of computer technology (SPSS). The inductive analysis commenced with a case study of a single pupil, Lorraine. This provided the reference point for the structured analysis of bullying issues in the wider context of the school. Findings include: 0 the differing ways that bullying was defined by the parties; 0 the emergent distinction between a relationship that was founded on bullying and an action that might be described as bullying; 0 that bullying usually occurred between pupils in the same class and was not a clandestine activity nor unknown to non-participants (the secretive image); 0 that, although there was a degree of satisfaction reported by all parties concerning methods deployed in handling bullying, there was also inconsistency, confusion and a lack of awareness of policy.University of Plymout

An investigation into the feasibility of the integration of microwave circuitry into a woven textile

To investigate the integration of a textile antenna into a woven substrate at the point of production. The antenna was to have the characteristics of a conventional fabric interms of the handle and drape