Extremal maps of the universal hyperbolic solenoid

We show that the set of points in the Teichmuller space of the universal hyperbolic solenoid which do not have a Teichmuller extremal representative is generic (that is, its complement is the set of the first kind in the sense of Baire). This is in sharp contrast with the Teichmuller space of a Riemann surface where at least an open, dense subset has Teichmuller extremal representatives. In addition, we provide a sufficient criteria for the existence of Teichmuller extremal representatives in the given homotopy class. These results indicate that there is an interesting theory of extremal (and uniquely extremal) quasiconformal mappings on hyperbolic solenoids.Comment: LaTeX, 15 page

Convex regions in the plane and their domes

We make a detailed study of the relation of a euclidean convex region $\Omega \subset \mathbb C$ to $\mathrm{Dome} (\Omega)$. The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of $\Omega$. The first result is to prove that the nearest point retraction $r: \Omega \to \mathrm{Dome} (\Omega)$ is 2-quasiconformal. The second is to establish precise estimates of the distortion of $r$ near $\partial \Omega$

Cost-effectiveness of treatments for superficial venous refluxin patients with chronic venous ulceration.

Background Venous leg ulcers impair quality of life significantly, with substantial costs to health services. The aim of this study was to estimate the cost‐effectiveness of interventional procedures alongside compression therapy versus compression therapy alone for the treatment of chronic venous leg ulceration. Methods A Markov decision analytical model was developed. The main outcome measures were quality‐adjusted life‐years (QALYs) and lifetime costs per patient, from the perspective of the UK National Health Service at 2015 prices. Resource use included the initial procedures, compression therapy, primary care and outpatient consultations. The interventional procedures included superficial venous surgery, endothermal ablation and ultrasound‐guided foam sclerotherapy (UGFS). The study population was patients with a chronic venous ulcer who were eligible for either compression therapy or an interventional procedure. Data were obtained from systematic review and meta‐analysis of RCTs. Results Surgery gained 0·112 (95 per cent c.i. −0·011 to 0·213) QALYs compared with compression therapy alone, with a difference in lifetime costs of €−1330 (−3570 to 1262). Given the expected savings in community care, the procedure would pay for itself within 4 years. There was insufficient evidence regarding endothermal ablation and UGFS to draw conclusions. Discussion This modelling study found surgery to be more effective and less costly than compression therapy alone. Further RCT evidence is required for both endothermal ablation and UGFS

Pseudo-Riemannian geodesic foliations by circles

We investigate under which assumptions an orientable pseudo-Riemannian geodesic foliations by circles is generated by an $S^1$-action. We construct examples showing that, contrary to the Riemannian case, it is not always true. However, we prove that such an action always exists when the foliation does not contain lightlike leaves, i.e. a pseudo-Riemannian Wadsley's Theorem. As an application, we show that every Lorentzian surface all of whose spacelike/timelike geodesics are closed, is finitely covered by $S^1\times \R$. It follows that every Lorentzian surface contains a non-closed geodesic.Comment: 14 page

Photovoltaic effect in ferroelectric ceramics

The ceramic structure was simulated in a form that is more tractable to correlation between experiment and theory. Single crystals (of barium titanate) were fabricated in a simple corrugated structure in which the pedestals of the corrugation simulated the grain while the intervening cuts could be filled with materials simulating the grain boundaries. The observed photovoltages were extremely small (100 mv)

Ferrite post in a rectangular wave guide

A thin circular ferrite post magnetized lengthwise is placed in a rectangular wave guide with its axis normal to the direction of propagation of the incident waves. The polarization is such that the electric vector is parallel to the post. The reflected and transmitted waves are calculated both with respect to their intensities and phases. The results are also applied to find the influence of a thin ferrite post upon the resonant frequency of a rectangular cavity

On Epstein's trajectory model of non-relativistic quantum mechanics

In 1952 Bohm presented a theory about non-relativistic point-particles moving along deterministic trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm's particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement