Yang-Baxter maps and the discrete KP hierarchy

We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with regard to the symmetry algebra underlying the reduced systems as well as the ultradiscretizability of these systems are discussed. A scheme for constructing ultradiscretizable reductions that give rise to Yang–Baxter maps is explained in two explicit examples

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

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

Materialities of clinical handover in intensive care: challenges of enactment and education

Abstract The research is situated in a busy intensive care unit in a tertiary referral centre university hospital in Scotland. To date no research appears to have been done with a focus on handover in intensive care, across the professions involved, examining how handover is enacted. This study makes an original contribution to the practical and pedagogical aspects of handover in intensive care both in terms of the methodology used and also in terms of its findings. In order to study handover a mixed methods approach has been adopted and fieldwork has been done in the ethnographic mode. Data has been audio recorded and transcribed and analysed to explore the clinical handovers of patients by doctors and nurses in this intensive care unit. Texts of both handover, and the artefacts involved, are reviewed. Material from journals, books, lectures and websites, including those for health care professionals, patients and relatives, and those in industry are explicated. This study explores the role of material artefacts and texts, such as the intensive care-based electronic patient record, the whiteboards in the doctors’ office, and in the ward, in the enactment of handover. Through analysis of the data I explore some of the entanglements and ontologies of handover and the multiple things of healthcare: patients, information, equipment, activities, texts, ideas, diseases, staff, diagnoses, illnesses, floating texts, responsibility, a plan, a family. The doing of handover is framed theoretically through the empirical philosophy of Mol’s identification of multiple ontologies in clinical practice (Mol, 2002). Each chapter is prefaced by a poem, each of which has relevant socio-material elements embedded in it. The significance of the findings of the research for both patient care and clinical education and learning is surfaced

COLONIZATION AND CULTURAL INTERACTION: EXPLORING THE EXPRESSION AND CONTINUATION OF ETHNIC IDENTITY IN SPANISH COLONIAL FEMALE RELIGIOUS INSTITUTIONS

Na discussão sobre a colonização espanhola da América Latina, é fundamental levar em consideração o impacto da Igreja Católica sobre as colônias espanholas. Instituições religiosas influenciaram vários aspectos da sociedade colonial, incluindo a economia, o sistema político e a ideologia. Conventos são espaços interessantes para explorar os mecanismos de colonização, pois não só mantiveram as ideologias raciais e de classe trazidos da Espanha, mas também forneceram uma base moral e religiosa para a presença colonial. As freiras participavam ativamente no desenvolvimento e manutenção da sociedade de elite espanhola.

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Resolving the decades-long transient FIRST J141918.9+394036: an orphan long gamma-ray burst or a young magnetar nebula?

Ofek (2017) identified FIRST J141918.9+394036 (hereafter FIRST J1419+3940) as a radio source sharing similar properties and host galaxy type to the compact, persistent radio source associated with the first known repeating fast radio burst, FRB 121102. Law et al. (2018) showed that FIRST J1419+3940 is a transient source decaying in brightness over the last few decades. One possible interpretation is that FIRST J1419+3940 is a nearby analogue to FRB 121102 and that the radio emission represents a young magnetar nebula (as several scenarios assume for FRB 121102). Another interpretation is that FIRST J1419+3940 is the afterglow of an `orphan' long gamma-ray burst (GRB). The environment is similar to where most such events are produced. To distinguish between these hypotheses, we conducted radio observations using the European VLBI Network at 1.6 GHz to spatially resolve the emission and to search for millisecond-duration radio bursts. We detect FIRST J1419+3940 as a compact radio source with a flux density of $620 \pm 20\ \mathrm{\mu Jy}$ (on 2018 September 18) and a source size of $3.9 \pm 0.7\ \mathrm{mas}$ (i.e. $1.6 \pm 0.3\ \mathrm{pc}$ given the angular diameter distance of $83\ \mathrm{Mpc}$). These results confirm that the radio emission is non-thermal and imply an average expansion velocity of $(0.10 \pm 0.02)c$. Contemporaneous high-time-resolution observations using the 100-m Effelsberg telescope detected no millisecond-duration bursts of astrophysical origin. The source properties and lack of short-duration bursts are consistent with a GRB jet expansion, whereas they disfavor a magnetar birth nebula.Comment: 8 pages, 4 figures, accepted for publication in ApJ

Atmospheric Deposition: A Potential Source of Trace Metal Organic Complexing Ligands to the Marine Environment

The present study confirms the existence of rainwater and seawater soluble metal (Cu, Pb, Cd, Ni and Co) complexing organic ligands associated with end-member aerosol populations. The end member aerosols being representative of a European urban aerosol population (LUAP ¿ Liverpool Urban Aerosol Population), and an aerosol population representative of crustal dominated material (Mesh Saharan dust, collected off the west African coast). The investigations carried out by ACSV (adsorptive cathodic stripping voltammetry) clearly indicated that these end-members were a source of organic complexing ligands for all the considered metals. For LUAP Cu 26%, Pb 55%, Cd 36%, Ni 26% and Co 27% of the total seawater soluble fraction was ACSVnon-labile (i.e. that fraction of the dissolved metal which is released after UV irradiation) compared to the corresponding values for Saharan dust (Cu 59%, Pb 23%, Cd 56%, Ni 66%, Co 23%). From these studies it was apparent that the dissolution for all metals and their respective fractions in both seawater and artificial rainwater was a rapid process with no further release after ca. 30 minutes. The studies displayed for a number of the metals re-adsorption of ACSVnon-labile metal to the aerosol particulate surface (Co and Pb - Saharan / seawater; Co and Cd - LUAP / seawater) implying that different geochemical pathways are taken by different metal speciation fractions leading to potential differences in their marine residence times. Conditional formation stability constants and complexing capacities for Ni were determined for seawater after being equilibrated with both end member aerosols. Log K\u27NiL detected were 18.3 - 0.3 and 19.26 - 0.4 for LUAP and Saharan dust respectively. The equivalent complexing capacities were 1.0 - 0.1 nmol mg-1 and 0.038 - 0.005 nmol mg-1 respectively