Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

Dispersive estimates for Schr\"odinger operators with point interactions in R3\mathbb{R}^3

The study of dispersive properties of Schr\"odinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schr\"odinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p-L^q$ estimates of the free Laplacian in the smaller regime $q\in[2,3)$. These estimates are implied by a recent result concerning the $L^p$ boundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q\geq 3$.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201

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

L^p boundedness of the wave operator for the one dimensional Schroedinger operator

Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the wave operators are bounded operators on L^p for all 1<p<\infty, provided (1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a resonance. For p=\infty we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.Comment: 26 page

Interpolation Theorems for Self-adjoint Operators

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where $L$ is a uniformly elliptic operator or a Schr\"odinger operator with electro-magnetic potential.Comment: 8 pages. Submitte

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

Risk factors for death from invasive pneumococcal disease, europe, 2010

We studied the possible association between patient age and sex, clinical presentation, Streptococcus pneumoniae serotype, antimicrobial resistance, and death in invasive pneumococcal disease cases reported by 17 European countries during 2010. The study sample comprised 2,921 patients, of whom 56.8% were men and 38.2% were >65 years of age. Meningitis occurred in 18.5% of cases. Death was reported in 264 (9.0%) cases. Older age, meningitis, and nonsusceptibility to penicillin were signifcantly asso ciated with death. Non-pneumococcal conjugate vaccine (PCV) serotypes among children 65 years of age, risk did not differ by serotype. These fndings highlight differences in case-fatality rates between sero types and age; thus, continued epidemiologic surveillance across all ages is crucial to monitor the long-term effects of PCVs

Truth after post-truth: for a Strong Programme in Discourse Studies

Contemporary post-truth discourses put the constructivist foundations of Discourse Studies to a test. According to critical observers, discourse analysts have been playing into the hands of Trump, Brexit and right-wing populists by politicising scientific knowledge and undermining the idea of scientific truth. In order to respond to these concerns, this article outlines a Strong Programme in Discourse Studies. While the Strong Programme insists on truths as discursive constructions, in no way does it claim that all ideas have the same truth value or that an idea can become true because somebody wants it to be true. The Strong Programme makes the case for discourse research that is constructivist (it asks how truths are constructed practically) without being relativist (all ideas do not have the same normative quality). Taking inspiration from debates in Science and Technology Studies of the 1970s, the Strong Programme formulates principles for discourse researchers dealing with conflicting truth claims. Discourse analytical explanations of truths of first-order participants and of second-order observers should be symmetrical, heterogeneous, multi-perspectival and reflexive. The Strong Programme discourse research is grounded in the founding traditions of ?French? and ?Critical? Discourse Studies, which have struggled over questions of truth and reality since the beginning. While critically interrogating the structuralist heritage of these strands, the Strong Programme insists on the practices of making and unmaking ideas through language use no matter whether they appear as true or false to participants and observers. Discourse Studies are encouraged to critically reflect on how hierarchies between knowledges are not only represented but, through their representation, also constituted through discursive practices