Criteria for solvable radical membership via p-elements

Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable radical of a finite group $G$ can be characterized as the set of all $x\in G$ such that is solvable for all $y\in G$. We prove two generalizations of this result. Firstly, it is enough to check the solvability of for every $p$-element $y\in G$ for every odd prime $p$. Secondly, if $x$ has odd order, then it is enough to check the solvability of $$ for every 2-element $y\in G$.Comment: 17 page

Service innovation for living well with type 1 Diabetes

The UK’s NHS must evolve to embrace the co-production of health outcomes and patient-centred care to shift from the reductive treatment of illness to a holistic promotion of wellness. We are developing a methodology for service innovation building on this. Designing innovative services for young people with type 1 diabetes surfaced different views of wellness from health professionals, young people and their parents. Our challenge has been to value each perspective in what we have designed. Deploying artefacts enabled constructive dialogue with our participants, so how might interactive artefacts challenge views of wellness

Aggregate Growth and the Efficiency of Labour Reallocation

We consider the potential importance of labour market efficiency for aggregate growth. The idea is that efficient labour markets move workers more quickly from low to high productivity sites, thereby raising aggregate productivity growth. We define a measure of labour market efficiency as a structural parameter from a matching function. Using labour market data on 15 OECD countries, we estimate this and show that it has a significant effect on growth. The results are robust to a number of different estimation techniques. The quantitative impact of market efficiency is not trivial.growth, labour market efficiency, labour market institutions

Different views : including others in participatory health service innovation

We describe our experiences employing experience-based design (EBD) to improve an outpatients health service in the UK and discuss the impacts of incorporating the voices of those not directly using or working within the service. We suggest that such new perspectives, experiences and expertise may enable the development of service innovations outside patients’ and staffs’ conceptual space of problems/solutions, but can affect the ownership and agency within the change project. To conclude, we propose a balance between accomplishing change and creating the self-belief to achieve it

The Limited Diagnosticity of Criminal Trials

Few political institutions play as palpable, ubiquitous, and solemn a role in the U.S. public life as the criminal justice system. The task of determining the defendant\u27s criminal liability with a high degree of certitude is performed through the ritualized and highly proceduralized adjudicative process, with the trial at its core. The United States Supreme Court has portrayed the criminal trial as a decisive and portentous and paramount event. Trials are considered the central institution of law as we know it, the crown jewel of the legal system. Amidst its multiple purposes, an essential objective of the criminal trial is to determine facts: which human events constitute crimes and who perpetrated them. Specifically, the trial is designed to serve the diagnostic function of distinguishing between prosecutions of guilty and innocent people, or at least between compelling prosecutions and those that do not meet the requisite certitude. The prevailing sentiment within the American polity and legal profession is that the trial is indeed acutely diagnostic. Naturally, the potential for accurate criminal verdicts depends on the ability of the factfinders-typically juries-to ascertain the facts accurately. The Supreme Court routinely lauds the process\u27s factfinding capabilities

Pilot-scale spiral wound membrane assessment for THM precursor rejection from upland waters

The outcomes of a pilot-scale study of the rejection of trihalomethanes (THMs) precursors by commercial ultrafiltration/nanofiltration (UF/NF) spiral-wound membrane elements are presented based on a single surface water source in Scotland. The study revealed the expected trend of increased flux and permeability with increasing pore size for the UF membranes; the NF membranes provided similar fluxes despite the lower nominal pore size. The dissolved organic carbon (DOC) passage decreased with decreasing molecular weight cut-off, with a less than one-third the passage recorded for the NF membranes than for the UF ones. The yield (weight % total THMs per DOC) varied between 2.5% and 8% across all membranes tested, in reasonable agreement with the literature, with the aromatic polyamide membrane providing both the lowest yield and lowest DOC passage. The proportion of the hydrophobic (HPO) fraction removed was found to increase with decreasing membrane selectivity (increasing pore size), and THM generation correlated closely (R2 = 0.98) with the permeate HPO fractional concentration