‘Nobody could possibly misunderstand what a group is’: a study in early twentieth-century group axiomatics

In the early years of the twentieth century, the so-called ‘postulate analysis’—the study of systems of axioms for mathematical objects for their own sake—was regarded by some as a vital part of the efforts to understand those objects. I consider the place of postulate analysis within early twentieth-century mathematics by focusing on the example of a group: I outline the axiomatic studies to which groups were subjected at this time and consider the changing attitudes towards such investigations

The ATLAS experiment at the CERN Large Hadron Collider: a description of the detector configuration for Run 3

Abstract The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of  ℒ = 2 × 1034 cm-2 s-1 was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of  ℒ = 2 × 1034 cm-2 s-1, with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector.</jats:p

The ATLAS experiment at the CERN Large Hadron Collider: a description of the detector configuration for Run 3

Abstract The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of  ℒ = 2 × 1034 cm-2 s-1 was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of  ℒ = 2 × 1034 cm-2 s-1, with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector.</jats:p