Darboux dressing and undressing for the ultradiscrete KdV equation

We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show how to reconstruct the potential in the scattering problem at any time, using an ultradiscrete analogue of a Darboux transformation. This is achieved by obtaining data uniquely characterising the soliton content and the `background' from the initial potential by Darboux transformation.Comment: 41 pages, 5 figures // Full, unabridged version, including two appendice

Evolution of Broad-line Emission from Active Galactic Nuclei

Apart from viewing-dependent obscuration, intrinsic broad-line emission from active galactic nuclei (AGNs) follows an evolutionary sequence: Type $1 \to 1.2/1.5 \to 1.8/1.9 \to 2$ as the accretion rate onto the central black hole is decreasing. This spectral evolution is controlled, at least in part, by the parameter $L_{\rm bol}/M^{2/3}$, where $L_{\rm bol}$ is the AGN bolometric luminosity and $M$ is the black hole mass. Both this dependence and the double-peaked profiles that emerge along the sequence arise naturally in the disk-wind scenario for the AGN broad-line region.Comment: MNRAS, to be publishe

Economical genotyping of little blue penguin (Eudyptula minor) clades from feather-based DNA

Determination of clade membership is a crucial requirement for many research questions addressing phylogeography, population structure, mating patterns, speciation, and hybridisation. The little blue penguin (Eudyptula minor) can be separated into two deeply divergent clades. However, assigning clade membership in little blue penguins requires molecular methods. Genetic sequencing can be used to identify clade membership but is expensive. Here, we present an economical alternative to the use of sequencing to determine little blue penguin clade membership. We extracted DNA from feathers using a method that produced reasonable quantities of DNA. We then amplified the D-loop section of the mitochondrial control region from total genomic DNA extracts, using the primers 'C L-tRNAglu' and 'D H-Dbox' followed by digestion with the restriction enzyme AluI. When visualised on a gel, distinctive banding patterns clearly indicated clade membership. We sequenced a subset of our samples and verified the accuracy of this method. The methods we present should facilitate little blue penguin research through a cost-effective approach to clade analysis as well as a successful technique to extract DNA from feathers when blood or tissue samples are not available

Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations

We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard