Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Tactical interventions in online hate speech : the case of #stopIslam

This article sets out findings from a project focused on #stopIslam, a hashtag that gained prominence following the Brussels terror attack of 2016. We initially outline a big data analysis which shows how counter-narratives – criticizing #stopIslam – momentarily subverted negative news reporting of Muslims. The rest of the article details qualitative findings that complicate this initial positive picture. We set out key tactics engaged in by right-wing actors, self-identified Muslim users, would-be allies and celebrities and elucidate how these tactics were instrumental in the direction, dynamics and legacies of the hashtag. We argue that the tactical interventions of tightly bound networks of right-wing actors, as well as the structural constraints of the platform, not only undermined the longevity and coherence of the counter-narratives but subtly modulated the affordances of Twitter in ways that enabled these users to extend their voice outwards, reinforcing long-standing representational inequalities in the process

Michael Gove’s war on professional historical expertise : conservative curriculum reform, extreme Whig history and the place of imperial heroes in modern multicultural Britain

Six years of continuously baiting his opponents within the history profession eventually amounted to little where it mattered most. UK Secretary of State for Education, Michael Gove, finally backtracked in 2013 on his plans to impose a curriculum for English schools based on a linear chronology of the achievements of British national heroes. His ‘history as celebration’ curriculum was designed to instil pride amongst students in a supposedly shared national past, but would merely have accentuated how many students in modern multicultural Britain fail to recognise themselves in what is taught in school history lessons. Now that the dust has settled on Gove’s tenure as Secretary of State, the time is right for retrospective analysis of how his plans for the history curriculum made it quite so far. How did he construct an ‘ideological’ conception of expertise which allowed him to go toe-to-toe for so long with the ‘professional’ expertise of academic historians and history teachers? What does the content of this ideological expertise tell us about the politics of race within Conservative Party curriculum reforms? This article answers these questions to characterise Gove as a ‘whig historian’ of a wilfully extreme nature in his attachment to imperial heroes as the best way to teach national history in modern multicultural Britain

A time-frequency analysis perspective on Feynman path integrals

The purpose of this expository paper is to highlight the starring role of time-frequency analysis techniques in some recent contributions concerning the mathematical theory of Feynman path integrals. We hope to draw the interest of mathematicians working in time-frequency analysis on this topic, as well as to illustrate the benefits of this fruitful interplay for people working on path integrals.Comment: 26 page

Year in review in Intensive Care Medicine 2009: II. Neurology, cardiovascular, experimental, pharmacology and sedation, communication and teaching

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Swimming physiology of European silver eels (Anguilla anguilla L.): energetic costs and effects on sexual maturation and reproduction

The European eel migrates 5,000–6,000 km to the Sargasso Sea to reproduce. Because they venture into the ocean in a pre-pubertal state and reproduce after swimming for months, a strong interaction between swimming and sexual maturation is expected. Many swimming trials have been performed in 22 swim tunnels to elucidate their performance and the impact on maturation. European eels are able to swim long distances at a cost of 10–12 mg fat/km which is 4–6 times more efficient than salmonids. The total energy costs of reproduction correspond to 67% of the fat stores. During long distance swimming, the body composition stays the same showing that energy consumption calculations cannot be based on fat alone but need to be compensated for protein oxidation. The optimal swimming speed is 0.61–0.67 m s−1, which is ~60% higher than the generally assumed cruise speed of 0.4 m s−1 and implies that female eels may reach the Sargasso Sea within 3.5 months instead of the assumed 6 months. Swimming trials showed lipid deposition and oocyte growth, which are the first steps of sexual maturation. To investigate effects of oceanic migration on maturation, we simulated group-wise migration in a large swim-gutter with seawater. These trials showed suppressed gonadotropin expression and vitellogenesis in females, while in contrast continued sexual maturation was observed in silver males. The induction of lipid deposition in the oocytes and the inhibition of vitellogenesis by swimming in females suggest a natural sequence of events quite different from artificial maturation protocols