Motivic Atiyah-Segal completion theorem

Let T be a torus, X a smooth separated scheme of finite type equipped with a T -action, and [X/T] the associated quotient stack. Given any localizing A1 -homotopy invariant of dg categories E (homotopy K -theory, algebraic K -theory with coefficients, étale K -theory with coefficients, l -adic algebraic K -theory, l -adic étale K -theory, semi-topological K -theory, topological K -theory, periodic cyclic homology, etc), we prove that the derived completion of E([X/T]) at the augmentation ideal I of the representation ring R(T) of T agrees with the classical Borel construction associated to the T -action o X⁠. Moreover, for certain localizing A1 -homotopy invariants, we extend this result to the case of a linearly reductive group scheme G⁠. As a first application, we obtain an alternative proof of Krishna’s completion theorem in algebraic K-theory, of Thomason’s completion theorem in étale K -theory with coefficients, and also of Atiyah-Segal’s completion theorem in topological K -theory (for those topological M -spaces Xan arising from analytification; M is a(ny) maximal compact Lie subgroup of Gan⁠). These alternative proofs lead to a spectral enrichment of the corresponding completion theorems and also to the following improvements: in the case of Thomason’s completion theorem the base field k no longer needs to be separably closed, and in the case of Atiyah-Segal’s completion theorem the topological M -space Xan no longer needs to be compact and the M -equivariant topological K -theory groups of Xan no longer need to be finitely generated over the representation ring R(M) ⁠. As a second application, we obtain new completion theorems in l -adic étale K -theory, in semi-topological K -theory and also in periodic cyclic homology. As a third application, we obtain a description of the different equivariant cohomology groups in the literature (motivic, l-adic, morphic, Betti, de Rham, etc) in terms of derived completion. Finally, in two appendixes of independent interest, we extend a result of Weibel on homotopy K -theory from the realm of schemes to the broad setting of quotient stacks and establish some useful properties of semi-topological K -theory

Transformers : transformed to transform - global mini cases in AI, healthcare and manufacturing

This case study consists of three mini cases that feature women leaders in different industry contexts. The cases highlight crucible moments for each leader, the influence of context on leadership style, gendered barriers, and opportunities to women's leadership. This case study presents opportunities for critical analysis of known leadership frameworks and opportunities for reflection on contemporary leadership needs

Classroom as crucible in the Humboldtian university : Reply to Collin

This reply to Finn Collin’s critically sympathetic review of my Back to the University’s Future: The Second Coming of Humboldt, addresses some of the tensions involved in realizing “Humboldt 2.0” in today’s higher education environment. Its focus is largely on the academic’s sense of researcher as being one of learner. In other words, the Humboldtian sees research as the necessary complement to teaching, not something radically distinct from it

Elucidating gas evolution of Prussian white cathodes for sodium‐ion battery application : the effect of electrolyte and moisture

As global energy storage demand increases, sodium-ion batteries are often considered as an alternative to lithium-ion batteries. Hexacyanoferrate cathodes, commonly referred to as Prussian blue analogues (PBAs), are of particular interest due their low-cost synthesis and promising electrochemical response. However, because they consist of ~50 wt% cyanide anions, a possible release of highly toxic cyanide gases poses a significant safety risk. Previously, we observed the evolution of (CN)2 during cycling via differential electrochemical mass spectrometry (DEMS), but were unable to determine a root cause or mechanism. In this work, we present a systematical investigation of the gas evolution of Prussian white (PW) with different water content via DEMS. While H2 is the main gas detected, especially in hydrated PW and during overcharge (4.6 V vs. Na+/Na), the evolution of CO2 and (CN)2 depends on the electrolyte conductive salt. The use of oxidative NaClO4 instead of NaPF6 is the leading cause for the formation of (CN)2. Mass spectrometric evidence of trace amounts of HCN is also found, but to a much lower extent than (CN)2, which is the dominant safety risk when using NaClO4-containing electrolyte, which despite being a good model salt, is not a viable option for commercial applications

Mainstream and special schools’ use of well-being programmes : a regional survey

The incorporation of mental well-being provision into school curricula is increasingly the focus of government policy in the UK and internationally. However, it is not clear what well- being programmes schools provide to pupils, and how these programmes are delivered. The current study was an online survey to assess the use of whole-school well-being programmes in primary schools in North Wales. Normalisation Process Theory (NPT) was utilised as a framework to assess normalisation of the well-being programmes. One-hundred and fifty-one schools in North Wales responded to the survey. The mean number of whole-school well- being programmes utilised by schools was 4.59, and nine of the ten most frequently used programmes had little or no associated evidence base. The well-being programmes were generally perceived as normalised (i.e., everyday practice) by respondents. Implications for future practice are discussed, including the need to support schools to identify and implement evidence-based mental well-being provision

COVID-19 vaccine refusal as unfair free-riding

Contributions to COVID-19 vaccination programmes promise valuable collective goods. They can support public and individual health by creating herd immunity and taking the pressure off overwhelmed public health services; support freedom of movement by enabling governments to remove restrictive lockdown policies; and improve economic and social well-being by allowing businesses, schools, and other essential public services to re-open. The vaccinated can contribute to the production of these goods. The unvaccinated, who benefit from, but who do not contribute to these goods can be morally criticised as free-riders. In this paper defends the claim that in the case of COVID-19, the unvaccinated are unfair free-riders. I defend the claim against two objections. First, that they are not unfair free-riders because they lack the subjective attitudes and intentions of free-riders; second, that although the unvaccinated may be free-riders, their free-riding is not unfair. [Abstract copyright: © 2024. The Author(s).

Magnetic structure, excitations, and field-induced transitions in the honeycomb lattice compound Er2Si2O7

We investigate the magnetic properties of the monoclinic D-type Er2Si2O7 with a distorted honeycomb lattice using powder and single-crystal neutron scattering techniques, as well as single-crystal magnetization measurements. The powder neutron diffraction shows that below the ordering temperature, TN=1.85K, the compound forms a q=0 antiferromagnetic structure with four sublattices. For H∥a, magnetization measurements reveal a narrow but clearly visible plateau at one-third of the magnetization saturation value. The plateau's stabilization is accompanied by a significant increase of the magnetic unit cell, as the magnetic peaks with fractional indices are observed in single-crystal neutron diffraction experiments. At low temperatures, the inelastic neutron scattering measurements reveal the presence of low-energy, almost dispersionless excitations. Their spectrum is sensitive to the applied field, it significantly softens on the magnetization plateau, and demonstrates the behavior expected for a noncollinear Ising antiferromagnet away from the plateau

Effects of delayed testing on decisions to stop learning

This study explores whether people’s preference to restrict to-be-learned material is influenced by memory test timing. In Experiments 1a and 2a, participants studied word lists. For control groups, lists were displayed in their entirety, whereas participants in other groups could stop the lists early. We investigated whether participants decided to terminate learning when they expected their free-recall memory to be tested after a short (Experiment 1a) or long (Experiment 2a) delay. Experiments 1b and 2b tested participants’ theoretical assumptions about learning termination. Participants who terminated learning recalled fewer words than those who saw all to-be-remembered materials. When the memory test immediately followed the learning phase, more than half of the participants decided to stop learning. However, when there was any time delay between learning and testing, only around a quarter of them decided to stop. Delayed testing can effectively discourage a maladaptive learning strategy of learning termination