Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page

Non-equilibrium Lorentz gas on a curved space

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries

Techniques for the Collection and Assay of Sleep Promotion Factor in Exercised and Sleep Deprived Dogs

v, 45 leaves. Advisor: Donald B. StrattonThe problem. The Pieron Phenomenon is the production of sleep in fully rested animals after a ventricular infusion of cerebrospinal fluid (CSF) from sleep deprived animals. According to the humoral theory of sleep, this is caused by the presentation of some sleep promoting substance (factor S) which depresses the brain. The somnolence produced is accompanied by an increase in slow wave sleep (SWS). Other factors which also increase SWS, such as exercise, may also do so through some mechanism involving the accumulation of factor S. Although this molecule is known to be a polypeptide with a molecular weight under 500, the structure remains unknown, greatly complicating the exploration of these relationships. Procedure. Schedules and equipment which permit controlled administration of exercise and sleep deprivation in dogs, and techniques for the removal and storage of CSF were developed and described. An assay procedure was described which makes use of the Pieron Phenomenon and the diurnal cycle of locomotor activity in rats. Summary. This paper describes several techniques which, when appropriately combined, can be incorporated into subsequent experiments measuring the effects of a variety of parameters on the productlon of sleep promotlng substance in the CSF

Relations Among Correlation Functions in the High Temperature Phase of QCD with Broken SU(3)

Group-theoretic arguments are used to determine the dependence of two-point correlators of quark bilinears on the current quark masses. The leading difference between $\pi$ and $\delta$ correlators is found to be of order $m_s$ times a U(1)$_{\scriptscriptstyle A}$-violating correlator. These general arguments are consistent with Schaefer's observation that if U(1)$_{\scriptscriptstyle A}$ violation persists to high enough temperatures then the strange $\eta$ can be lighter than the non-strange one.Comment: 8 page

Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.

Involvement of young people in a qualitative study that seeks to explore experiences of renal replacement therapy choice selection

Introduction: Patient and Public involvement (PPI) has become one of the drivers in health care and seen as an integral part of the research process. PPI promotes research questions that reflect the priorities and concerns of the relevant population and develops outcomes that are important to patients (INVOLVE, 2012; Evans et al, 2014; Hickey et al, 2018). Young adults with end-stage kidney disease are supported by clinicians and their families to make decisions about their preferred renal replacement therapy (NICE, 2018). However, they can become overwhelmed with the burden of long-term chronic illness and often struggle to accept diagnosis and prognosis and cope with the complex management of their condition (Coulter and Collins, 2011; Ritchie et al., 2012). They can consequently become disengaged with the service and less involved in their care (Ritchie et al, 2012; Robinski et al, 2014). The current study explores young people’s experiences of renal replacement therapy choice selection. The study team has involved young people in the study’s development. Aims and objectives: The aim of the involvement group in this study is to involve the young people in all stages of the research process: ensuring that the research question has the correct focus, that the participant information sheet is clear and that the recruitment strategy is appropriate. In due course, the young people’s group will be involved in qualitative data analysis and in dissemination of findings. Method: The involvement group comprised three people with experiences of dialysis and kidney transplant treatment as children and young adults. They were recruited via existing networks in the research team. A role description on what was to be expected of the group members was discussed, alongside what was expected from the research team (training and travel expenses for example). Communication is via face-to face meetings and also by email. This first face-to-face meeting discussed and shaped the research question, and the possible recruitment process. Further email discussions have explored the participant information sheet, consent forms plus the development of the video and poster advert to aid recruitment. Results: The impact of PPI on the research process is already providing valuable insights into how the research design should be conducted. The first face-to-face meeting with the group highlighted the difficulties that young people face when making choice of renal replacement therapy, especially psychosocial impact and mental well-being, so the impact the choice makes on well-being was added as a secondary research question. The acceptability of the recruitment method (via social media) was discussed and a video advert was developed for the recruitment process. Members also contributed to the review of some of the research documents; participant information sheet, consent forms, posters, research proposal and piloted a validation questionnaire for suitability. Impact: Involvement of patients helped situate the study to meet the current needs of young adults diagnosed with end stage renal disease who are faced with choosing dialysis or kidney transplantation