Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

RESPOND – A patient-centred program to prevent secondary falls in older people presenting to the emergency department with a fall: Protocol for a multi-centre randomised controlled trial

Introduction: Participation in falls prevention activities by older people following presentation to the Emergency Department (ED) with a fall is suboptimal. This randomised controlled trial (RCT) will test the RESPOND program which is designed to improve older persons’ participation in falls prevention activities through delivery of patient-centred education and behaviour change strategies. Design and setting: An RCT at two tertiary referral EDs in Melbourne and Perth, Australia. Participants: Five-hundred and twenty eight community-dwelling people aged 60-90 years presenting to the ED with a fall and discharged home will be recruited. People who: require an interpreter or hands-on assistance to walk; live in residential aged care or >50 kilometres from the trial hospital; have terminal illness, cognitive impairment, documented aggressive behaviour or history of psychosis; are receiving palliative care; or are unable to use a telephone will be excluded. Methods: Participants will be randomly allocated to the RESPOND intervention or standard care control group. RESPOND incorporates: (1) home-based risk factor assessment; (2) education, coaching, goal setting, and follow-up telephone support for management of one or more of four risk factors with evidence of effective intervention; and (3) healthcare provider communication and community linkage delivered over six months. Primary outcomes are falls and fall injuries per-person-year. Discussion: RESPOND builds on prior falls prevention learnings and aims to help individuals make guided decisions about how they will manage their falls risk. Patient-centred models have been successfully trialled in chronic and cardiovascular disease however evidence to support this approach in falls prevention is limited. Trial registration. The protocol for this study is registered with the Australian New Zealand Clinical Trials Registry (ACTRN12614000336684)

Guidelines for the treatment of postmenopausal osteoporosis for general practitioners

Copyright © 2002 Royal Australian College of General Practitioners Copyright to Australian Family Physician. Reproduced with permission. Permission to reproduce must be sought from the publisher, The Royal Australian College of General Practitioners.Background: Osteoporosis Australia has been committed to the education of general practitioners and the community with a series of updated guidelines on the management of osteoporosis. Since the last series was published in Australian Family Physician (August 2000), there have been further advances in our understanding of the treatments involved in both prevention of bone loss and the management of established osteoporosis. Objective: This article represents updated guidelines for the treatment of postmenopausal osteoporosis to assist GPs identify those women at risk and to review current treatment strategies. DISCUSSION: Osteoporosis and its associated problems are major health concerns in Australia, especially with an aging population. While important principles of management are still considered to be maximising peak bone mass and preventing postmenopausal bone loss, new clinical trial data about drugs such as the bisphosphonates, raloxifene and oestrogen have recently become available and the relative role of various agents is gradually becoming clearer. The use of long term hormone replacement therapy has mixed risks and benefits that requires individual patient counselling.O'Neill Sheila; Sambrook Philip; Diamond Terry; Ebeling Peter; Ferris Linda; Flicker Leon; Findlay David; Singh Maria Fiatarone; Lord Stephen; MacLennan Alastair; Markwell Alex; Nowson Caryl; Pocock Nick; Williamson Margare

Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system

Comparison of gas-phase free-radical populations in tobacco smoke and model systems by HPLC.

We used an improved method for trapping carbon-centered radicals (.R) from the gas-phase to compare radical suites trapped from various tobacco smoke and model smoke systems. Using a nitroxide trap, 3-amino-2,2,5,5-tetramethyl-1-pyrrolidinyloxy (3AP), on solid support, we trapped radicals directly from the gas phase, washed them off the support, and analyzed them with HPLC. Separation of the trapped radicals showed that each tobacco type produced a unique radical suite of 4-10 distinct peaks. Gas mixtures used to model tobacco smoke consisted of nitric oxide, air, isoprene, and methanol. The model systems produced radical suites of four major and several minor peaks, two of which matched peaks in tobacco smoke chromatograms. Quantities of radicals trapped from tobacco smoke were: 54 +/- 2 nmol .R per Marlboro cigarette, 66 +/- 9 nmol .R per Djarum clove cigarette, and 185 +/- 9 nmol .R per Swisher Sweet cigar. In these experiments oxygen competes with the nitroxide trap for gas-phase radicals. A kinetic analysis of the O2 competition shows that actual radical concentrations in the smoke were approximately 100-fold higher than measured

Classical Dimers on Penrose Tilings

We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead, their maximum matchings have a monomer density of $81-50\varphi\approx 0.098$ in the thermodynamic limit, with $\varphi=\left(1+\sqrt{5}\right)/2$ the golden ratio. Maximum matchings divide the tiling into a fractal of nested closed regions bounded by loops that cannot be crossed by monomers. These loops connect second-nearest neighbour even-valence vertices, each of which lies on such a loop. Assigning a charge to each monomer with a sign fixed by its bipartite sublattice, we find that each bounded region has an excess of one charge, and a corresponding set of monomers, with adjacent regions having opposite net charge. The infinite tiling is charge neutral. We devise a simple algorithm for generating maximum matchings, and demonstrate that maximum matchings form a connected manifold under local monomer-dimer rearrangements. We show that dart-kite Penrose tilings feature an imbalance of charge between bipartite sub-lattices, leading to a minimum monomer density of $\left(7-4\varphi\right)/5\approx 0.106$ all of one charge.Comment: 22+3 pages, 18+4 figure

A microscopic Ginzburg--Landau theory and singlet ordering in Sr2_2RuO4_4

The long-standing quest to determine the superconducting order of Sr$_2$RuO$_4$ (SRO) has received renewed attention after recent nuclear magnetic resonance (NMR) Knight shift experiments have cast doubt on the possibility of spin-triplet pairing in the superconducting state. As a putative solution, encompassing a body of experiments conducted over the years, a $d+ig$-wave order parameter caused by an accidental near-degeneracy has been suggested [S. A. Kivelson et al., npj Quantum Materials $\bf{5}$, 43 (2020)]. Here we develop a general Ginzburg--Landau theory for multiband superconductors. We apply the theory to SRO and predict the relative size of the order parameter components. The heat capacity jump expected at the onset of the second order parameter component is found to be above the current threshold deduced by the experimental absence of a second jump. Our results tightly restrict theories of $d+ig$ order, and other candidates caused by a near-degeneracy, in SRO. We discuss possible solutions to the problem.Comment: 13 pages, 8 figure