Relative Oscillation Theory for Dirac Operators

We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established. As an application we extend a result by K.M. Schmidt on the finiteness/infiniteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.Comment: 13 page

Calcareous concretions in the Levriere (tributary of the Epte, secondary tributary of the Seine, Eure department) [Translation from: Bull.Ass.fr.Etud.Quaternaire 1973(2), 79-87, 1973]

From research carried, out on a section of the Levriere, concretions (granules, nodules, which were sometimes joined together) partly covering the river ”bottom” were observed. The authors propose to make besides a petrographic examination of the calcareous precipitations and to see if their origin is connected to a biological activity, or if it is purely a case of a physical-chemical precipitation. The hydrological background of the Levriere, a small river of the Normandy Vexin, is given and conditions of the formation of the concretions studied

Evaluation of the impact of a low dose subcutaneous lignocaine and ketamine infusion utilising nerve excitability studies in a chronic migraine population.

Migraine is a common condition in which the diagnosis is based on clinical grounds. There is no clinically available biophysical marker that can evaluate migraine. Migraines are linked to functional brain changes in the absence of structural abnormalities. A clinically useful tool capable of evaluating functional changes in patients with migraine could be used to aid diagnosis and management. Patients with chronic migraine have frequent or continuous headache which is accompanied by significant morbidity. There are limited data available regarding treatment options for curtailment of chronic migraine. In this prospective observational study, patients suffering from chronic migraine underwent a prolonged subcutaneous lignocaine and ketamine infusion which has anecdotally been useful in management of chronic migraine. To determine if peripheral nerve excitability studies have a role in assessing patients with chronic migraine and their response to treatment, these studies were performed on patients before, during and after the infusion and at six months and compared to healthy age matched controls. Most patients (13/14) had significant clinical benefit from the infusion. No changes in excitability studies were identified in patients at baseline, during or after intervention with low-dose lignocaine/ketamine infusion. The lack of detectable change in excitability measurements despite significant clinical improvement resulting from the infusion may implicate a central mechanism of action of the infusion

I.—Notes on the Crinoidea

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"Strenuous Competition on the field of play, Diplomacy off it" – The 1908 London Olympics, Theodore Roosevelt, Arthur Balfour, and Transatlantic Relations

Through the lens of the 1908 Summer Olympic Games, and the sport-based ideals and philiospohies of the US president Roosevelt and the UK prime minister Balfour, this article explores the nature of transatlantic relations. It shows how views of sport cross into the political sphere and can be used in serious diplomatic relations and strategies