From First Lyapunov Coefficients to Maximal Canards

Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to calculate the location of a special trajectory, called a maximal canard, in parameter space. A first-order asymptotic expansion of this location was found by Krupa and Szmolyan in the framework of a "canard point"-normal-form for systems with one fast and one slow variable. We show how to compute the coefficient in this expansion using the first Lyapunov coefficient at the Hopf bifurcation thereby avoiding use of this normal form. Our results connect the theory of canard explosions with existing numerical software, enabling easier calculations of where canard explosions occur.Comment: preprint version - for final version see journal referenc

A theory of electromagnetism with uniquely defined potential and covariant conserved spin

A theory of electromagnetism is proposed that is based on the Fermi Lagrangian, which is symmetric under electromagnetic spin rotation. Its features are: - the four-potential is unambiguously determined by the inhomogeneous wave equation and boundary conditions at infinity. - the Lorenz condition and minimal coupling then follow from charge conservation. - electromagnetic spin is conserved and spin operators can be defined without sacrificing covariance. - quantisation is fully covariant, without redefining the metric. - all experimental predictions are the same as in the standard theory. This result proves that electromagnetic gauge invariance is redundant as a fundamental principle of physics.Comment: 4 pages, 1 figure, 20 equation

The story of Oh: the aesthetics and rhetoric of a common vowel sound

Studies in Musical Theatre is the only peer-reviewed journal dedicated to musical theatre. It was launched in 2007 and is now in its seventh volume. It has an extensive international readership and is edited by Dominic Symonds and George Burrows. This article investigates the use of the ‘word’ ‘Oh’ in a variety of different performance idioms. Despite its lack of ‘meaning’, the sound is used in both conversation and poetic discourse, and I discuss how it operates communicatively and expressively through contextual resonances, aesthetic manipulation and rhetorical signification. The article first considers the aesthetically modernist work of Cathy Berberian in Bussotti’s La Passion Selon Sade; then it considers the rhetorically inflected use of ‘Oh’ to construct social resonance in popular song;finally, it discusses two important uses of the sound ‘Oh’ which bookend the Broadway musical Oklahoma!, serving to consolidate the allegorical and musico-dramatic narrative of the show

Can anybody help? : mitigating IS development project risk with user

In this paper we aim to gain insight into the relationship between user participation modes and project risk factors, and then we construct a model that can be used to determine how user participation can be successfully applied in ISD projects with a given set of risk factors. We perform an in-depth literature review, which aims to clarify the concept of user participation as part of risk management. We then report on the results of a case study in Cap Gemini where we conduct an exploratory research of the application of user participation in practice. For this exploratory research, a quantitative and qualitative research method was designed in the form of a survey and interviews. Though the results from our case study we gain insight into the relationship between user participation and IS project risk and also determine how user participation can be used to mitigate such risk