Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

After Satan : Essays in Honour of Neil Forsyth

This volume is the result of a collective desire to pay homage to Neil Forsyth, whose work has significantly contributed to scholarship on Satan. This volume is "after" Satan in more ways than one, tracing the afterlife of both the satanic figure in literature and of Neil Forsyth's contribution to the field, particularly in his major books The Old Enemy: Satan and the Combat Myth (Princeton University Press, 1987, revised 1990) and The Satanic Epic (Princeton University Press, 2003). The essays in this volume draw on Forsyth's work as a focus for their analyses of literary encounters with evil or with the Devil himself, reflecting the richness and variety of contemporary approaches to the age-old question of how to represent evil. All the contributors acknowledge Neil Forsyth's influence in the study of both the Satan-figure and Milton's Paradise Lost. But beyond simply paying homage to Neil Forsyth, the articles collected here trace the lineage of the Satan figure through literary history, showing how evil can function as a necessary other against which a community may define itself. They chart the demonised other through biblical history and medieval chronicle, Shakespeare and Milton, to nineteenth-century fiction and the contemporary novel. Many of the contributors find that literary evil is mediated through the lens of the Satan of Paradise Lost, and their articles address the notion, raised by Neil Forsyth in The Satanic Epic, that the literary Devil-figures under consideration are particularly interested in linguistic ambivalence and the twisted texture of literary works themselves. The multiple responses to evil and the continuous reinvention of the devil figure through the centuries all reaffirm the textual presence of the Devil, his changing forms necessarily inscribed in the shifting history of western literary culture. These essays are a tribute to the work of Neil Forsyth, whose scholarship has illuminated and guided the study of the Devil in English and other literatures.

After Satan: Essays in Honour of Neil Forsyth

This volume is the result of a collective desire to pay homage to Neil Forsyth, whose work has significantly contributed to scholarship on Satan. This volume is "after" Satan in more ways than one, tracing the afterlife of both the satanic figure in literature and of Neil Forsyth's contribution to the field, particularly in his major books The Old Enemy: Satan and the Combat Myth (Princeton University Press, 1987, revised 1990) and The Satanic Epic (Princeton University Press, 2003). The essays in this volume draw on Forsyth's work as a focus for their analyses of literary encounters with evil or with the Devil himself, reflecting the richness and variety of contemporary approaches to the age-old question of how to represent evil. All the contributors acknowledge Neil Forsyth's influence in the study of both the Satan-figure and Milton's Paradise Lost. But beyond simply paying homage to Neil Forsyth, the articles collected here trace the lineage of the Satan figure through literary history, showing how evil can function as a necessary other against which a community may define itself. They chart the demonised other through biblical history and medieval chronicle, Shakespeare and Milton, to nineteenth-century fiction and the contemporary novel. Many of the contributors find that literary evil is mediated through the lens of the Satan of Paradise Lost, and their articles address the notion, raised by Neil Forsyth in The Satanic Epic, that the literary Devil-figures under consideration are particularly interested in linguistic ambivalence and the twisted texture of literary works themselves. The multiple responses to evil and the continuous reinvention of the devil figure through the centuries all reaffirm the textual presence of the Devil, his changing forms necessarily inscribed in the shifting history of western literary culture. These essays are a tribute to the work of Neil Forsyth, whose scholarship has illuminated and guided the study of the Devil in English and other literatures.

Friedman's Excess energy and the McMillan-Mayer theory of solutions:Thermodynamics

In his version of the theory of multicomponent systems, Friedman used the analogy which exists between the virial expansion for the osmotic pressure obtained from the McMillan-Mayer (MM) theory of solutions in the grand canonical ensemble and the virial expansion for the pressure of a real gas. For the calculation of the thermodynamic properties of the solution, Friedman proposed a definition for the"excess free energy" that is a reminder of the ancient idea for the"osmotic work". However, the precise meaning to be attached to his free energy is, within other reasons, not well defined because in osmotic equilibrium the solution is not a closed system and for a given process the total amount of solvent in the solution varies. In this paper, an analysis based on thermodynamics is presented in order to obtain the exact and precise definition for Friedman"s excess free energy and its use in the comparison with the experimental data.

Letter to Louis Cabot from S.D. Woodruff stating that he will sell his Point McMillen [McMillan], Michigan shares

Letter to Louis Cabot from S.D. Woodruff stating that he will sell his Point McMillen [McMillan], Michigan shares, but he doesn’t think that the sheriff will sell his Long Point shares, Jan. 6, 1886.

Letter to Louis Cabot from S.D. Woodruff regarding his Point McMillen [McMillan], Michigan shooting shares

Letter to Louis Cabot from S.D. Woodruff regarding his Point McMillen [McMillan], Michigan shooting shares. He says that he has decided to sell and his price is $3,000. He gives directions on how to get to the club which is on the Huron River, 7 miles from Rockwood, Jan. 25, 1886.

Femmes fatales en devenirs : les femmes vampires face à la domination masculine dans "Byzantium" (2012, Neil Jordan)

Ce mémoire est l'occasion d'établir une courte généalogie des femmes vampires au cinéma, en mettant en avant la manière dont la figure de la femme vampire résonne avec celle de la femme fatale, dans la mesure où elle constitue à la fois une vision négative de la femme émancipée, tout en offrant une manière d’échapper au modèle féminin traditionnel. En me demandant si le vampirisme peut être une source de pouvoir émancipatoire pour les femmes, j’analyse attentivement Byzantium (2012) de Neil Jordan. À travers l’étude successive des deux personnages principaux, Clara et Eleanor, je montre comment le film résonne avec la généalogie des femmes vampires établie préalablement, ainsi qu’avec certains enjeux féministes. Surtout, l’accent est mis sur la manière dont les personnages féminins contestent le pouvoir masculin, à travers la performance des stéréotypes, pour Clara, et la prise de contrôle du récit, pour Eleanor. Enfin, je me concentre sur la manière dont, à travers des mouvements de devenirs, ces personnages sortent du cycle fatal de l’oppression masculiniste, qui mène habituellement à l’extinction de la femme vampire en fin de récit, mais qui ici aboutit à une tentative de réconciliation entre les sexes. Mon travail s’appuie sur de larges recherches concernant la figure du vampire, ainsi que sur les études féministes et gender studies relatives aux textes vampiriques. Je m’appuie également sur les réflexions de Judith Butler, les travaux deleuziens sur la notion de « devenir », et les considérations de Derrida sur le don.

Obsessive Compulsive Treatment Efficacy Trial (OCTET) comparing the clinical and cost effectiveness of self-managed therapies: study protocol for a randomised controlled trial

Background: UK National Institute of Health and Clinical Excellence guidelines for obsessive compulsive disorder (OCD) specify recommendations for the treatment and management of OCD using a stepped care approach. Steps three to six of this model recommend treatment options for people with OCD that range from low-intensity guided self-help (GSH) to more intensive psychological and pharmacological interventions. Cognitive behavioural therapy (CBT), including exposure and response prevention, is the recommended psychological treatment. However, whilst there is some preliminary evidence that self-managed therapy packages for OCD can be effective, a more robust evidence base of their clinical and cost effectiveness and acceptability is required. Methods/Design: Our proposed study will test two different self-help treatments for OCD: 1) computerised CBT (cCBT) using OCFighter, an internet-delivered OCD treatment package; and 2) GSH using a book. Both treatments will be accompanied by email or telephone support from a mental health professional. We will evaluate the effectiveness, cost and patient and health professional acceptability of the treatments. Discussion: This study will provide more robust evidence of efficacy, cost effectiveness and acceptability of self-help treatments for OCD. If cCBT and/or GSH prove effective, it will provide additional, more accessible treatment options for people with OCD.

O realismo mágico nas Short Stories de Neil Gaiman, um contador de histórias da contemporaneidade

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