Singular open book structures from real mappings

We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus \Sing \psi \subset \psi^{-1}(0), for which the Milnor fibration exists and yields an open book structure with singular binding.Comment: more remark

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

The regulator, the Bloch group, hyperbolic manifolds, and the #eta#-invariant

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN033136 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Mixed Hodge Structures Applied to Singularities

We give a survey of applications of mixed Hodge theory to the study of isolated singularities. A summary of mixed Hodge theory is followed by some examples. The formalism of vanishing cycles is realized on the Hodge level by a sheaf complex with three filtrations, making the application to the cohomology of the Milnor fibre possible. The approaches by algebraic analysis and by motivic integration are discussed, and the spectrum with its properties is considered. The paper ends with a treatment of Du Bois singularities