Lensing and the Centers of Distant Early-Type Galaxies

Gravitational lensing provides a unique probe of the inner 10-1000 pc of distant galaxies (z=0.2-1). Lens theory predicts that every strong lens system should have a faint image near the center of the lens galaxy, which should be visible in radio lenses but have not been observed. We study these ``core'' images using models derived from the stellar distributions in nearby early-type galaxies. We find that realistic galaxies predict a remarkably wide range of core images, with lensing magnifications spanning some six orders of magnitude. More concentrated galaxies produce fainter core images, although not with any simple, quantitative, model independent relation. Some real galaxies have diffuse cores and predict bright core images (magnification mu>~0.1), but more common are galaxies that predict faint core images (mu<~0.001). Thus, stellar mass distributions alone are probably concentrated enough to explain the lack of observed core images, and may require observational sensitivity to improve by an order of magnitude before detections of core images become common. Two-image lenses will tend to have brighter core images than four-image lenses, so they will be the better targets for finding core images and exploiting these tools for studying the central mass distributions of distant galaxies.Comment: 13 pages, emulateapj; submitted to Ap

Forman's Ricci curvature - From networks to hypernetworks

Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name and the heavy reliance of combinatorial tools. We show that, in fact, a geometric unifying approach is possible, by viewing them as polyhedral complexes endowed with a simple, yet, the powerful notion of curvature - the Forman Ricci curvature. We systematically explore some aspects related to the modeling of weighted and directed hypernetworks and present expressive and natural choices involved in their definitions. A benefit of this approach is a simple method of structure-preserving embedding of hypernetworks in Euclidean N-space. Furthermore, we introduce a simple and efficient manner of computing the well established Ollivier-Ricci curvature of a hypernetwork.Comment: to appear: Complex Networks '18 (oral presentation

Inverse Compton Scattering as the Source of Diffuse EUV Emission in the Coma Cluster of Galaxies

We have examined the hypothesis that the majority of the diffuse EUV flux in the Coma cluster is due to inverse Compton scattering of low energy cosmic ray electrons (0.16 < epsilon < 0.31 GeV) against the 3K black-body background. We present data on the two-dimensional spatial distribution of the EUV flux and show that these data provide strong support for a non-thermal origin for the EUV flux. However, we show that this emission cannot be produced by an extrapolation to lower energies of the observed synchrotron radio emitting electrons and an additional component of low energy cosmic ray electrons is required.Comment: 11 pages, 5 figure

Topologically massive magnetic monopoles

We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, {\it a priory} completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics in the framework of the theory of Deser, Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a monopole solution

Toward a conceptual framework of emotional relationship marketing: an examination of two UK political parties

The purpose of this paper is to review the notion of branding and evaluate its applicability to political parties. As ideological politics is in decline, branding may provide a consistent narrative where voters feel a sense of warmth and belonging. The paper aims to build an understanding of the complexity of building a political brand where a combination of image, logo, leadership, and values can all contribute to a compelling brand narrative. It investigates how competing positive and negative messages attempt to build and distort the brand identity. A critical review of bran ding, relationship marketing, and political science literature articulates the conceptual development of branding and its applicability to political parties. The success or failure of negative campaigning is due to the authenticity of a political party’s brand values — creating a coherent brand story — if there is no distance between the brand values articulated by the political party and the values their community perceives then this creates an "authentic" brand. However, if there is a gap this paper illustrates how negative campaigning can be used to build a "doppelganger brand," which undermines the credibility of the authentic political brand. The paper argues that political parties need to understand how brand stories are developed but also how they can be used to protect against negative advertising. This has implications for political marketing strategists and political parties. This paper draws together branding theory and relationship marketing and incorporates them into a framework that makes a contribution to the political marketing literature

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu