A Nielsen theory for coincidences of iterates

As the title suggests, this paper gives a Nielsen theory of coincidences of iterates of two self maps f, g of a closed manifold. The ideas is, as much as possible, to generalize Nielsen type periodic point theory, but there are many obstacles. Many times we get similar results to the "classical ones" in Nielsen periodic point theory, but with stronger hypotheses.Comment: 30 page

Exploring the impact of the education led professionalisation agenda in policing: professional identity and engagement with continuing professional development (CPD)

Presentation to the PGRA conference in July 2023 on the position of my PhD by portfolio research as a part-time student in my second year. It set out the policing professionalisation agenda, the application of Bourdieu as the theoretical framework and the methods of data collection

Phase limitations of Zames-Falb multipliers

Phase limitations of both continuous-time and discrete-time Zames-Falb multipliers and their relation with the Kalman conjecture are analysed. A phase limitation for continuous-time multipliers given by Megretski is generalised and its applicability is clarified; its relation to the Kalman conjecture is illustrated with a classical example from the literature. It is demonstrated that there exist fourth-order plants where the existence of a suitable Zames-Falb multiplier can be discarded and for which simulations show unstable behavior. A novel phase-limitation for discrete-time Zames-Falb multipliers is developed. Its application is demonstrated with a second-order counterexample to the Kalman conjecture. Finally, the discrete-time limitation is used to show that there can be no direct counterpart of the off-axis circle criterion in the discrete-time domain

Measures of the solar spectral irradiance between 1200 and 3000 A

Tabulated data on solar flux measurements are presented. The measurements, taken from balloons, rockets and satellites, are not new data, but have been critically re-evaluated. The eleven year sunspot cycle is discussed. Also discussed is the brightness temperature. The effect of solar radiation at various wavelengths, on the photochemistry of stratospheric ozone is briefly discussed

Germanium quantum dots: Optical properties and synthesis

Three different size distributions of Ge quantum dots (>~200, 110, and 60 Å) have been synthesized via the ultrasonic mediated reduction of mixtures of chlorogermanes and organochlorogermanes (or organochlorosilanes) by a colloidal sodium/potassium alloy in heptane, followed by annealing in a sealed pressure vessel at 270 °C. The quantum dots are characterized by transmission electron microscopy, x-ray powder diffraction, x-ray photoemission, infrared spectroscopy, and Raman spectroscopy. Colloidal suspensions of these quantum dots were prepared and their extinction spectra are measured with ultraviolet/visible (UV/Vis) and near infrared (IR) spectroscopy, in the regime from 0.6 to 5 eV. The optical spectra are correlated with a Mie theory extinction calculation utilizing bulk optical constants. This leads to an assignment of three optical features to the E(1), E(0'), and E(2) direct band gap transitions. The E(0') transitions exhibit a strong size dependence. The near IR spectra of the largest dots is dominated by E(0) direct gap absorptions. For the smallest dots the near IR spectrum is dominated by the Gamma25-->L indirect transitions

Environments and Morphologies of Red Sequence Galaxies with Residual Star Formation in Massive Clusters

We present a photometric investigation into recent star formation in galaxy clusters at z ~ 0.1. We use spectral energy distribution templates to quantify recent star formation in large X-ray selected clusters from the LARCS survey using matched GALEX NUV photometry. These clusters all have signs of red sequence galaxy recent star formation (as indicated by blue NUV-R colour), regardless of cluster morphology and size. A trend in environment is found for these galaxies, such that they prefer to occupy low density, high cluster radius environments. The morphology of these UV bright galaxies suggests that they are in fact red spirals, which we confirm with light curves and Galaxy Zoo voting percentages as morphological proxies. These UV bright galaxies are therefore seen to be either truncated spiral galaxies, caught by ram pressure in falling into the cluster, or high mass spirals, with the photometry dominated by the older stellar population.Comment: Accepted for publication in MNRAS, 11 pages, 11 figure