Involution products in Coxeter groups

For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero

How do hospitals respond to feedback about blood transfusion practice? A multiple case study investigation

National clinical audits play key roles in improving care and driving system-wide change. However, effects of audit and feedback depend upon both reach (e.g. relevant staff receiving the feedback) and response (e.g. staff regulating their behaviour accordingly). This study aimed to investigate which hospital staff initially receive feedback and formulate a response, how feedback is disseminated within hospitals, and how responses are enacted (including barriers and enablers to enactment). Using a multiple case study approach, we purposively sampled four UK hospitals for variation in infrastructure and resources. We conducted semi-structured interviews with staff from transfusion-related roles and observed Hospital Transfusion Committee meetings. Interviews and analysis were based on the Theoretical Domains Framework of behaviour change. We coded interview transcripts into theoretical domains, then inductively identified themes within each domain to identify barriers and enablers. We also analysed data to identify which staff currently receive feedback and how dissemination is managed within the hospital. Members of the hospital’s transfusion team initially received feedback in all cases, and were primarily responsible for disseminating and responding, facilitated through the Hospital Transfusion Committee. At each hospital, key individuals involved in prescribing transfusions reported never having received feedback from a national audit. Whether audits were discussed and actions explicitly agreed in Committee meetings varied between hospitals. Key enablers of action across all cases included clear lines of responsibility and strategies to remind staff about recommendations. Barriers included difficulties disseminating to relevant staff and needing to amend feedback to make it appropriate for local use. Appropriate responses by hospital staff to feedback about blood transfusion practice depend upon supportive infrastructures and role clarity. Hospitals could benefit from support to disseminate feedback systematically, particularly to frontline staff involved in the behaviours being audited, and practical tools to support strategic decision-making (e.g. action-planning around local response to feedback)

Branding destinations: symbolic and narrative representations and co-branding

© 2019, Springer Nature Limited. This article explores the presence of symbolic and narrative representations on destination websites, and the explicit presence of co-branding in the form of partner logos. In contrast to previous research that tends to focus on case studies, this article adopts a survey approach. The study undertakes a content analysis of the websites of the 82 destinations identified on the VisitBritain website, including cities, regions, towns, villages and islands. On these websites, there is strong evidence of symbolic branding in the form of logos. However, less than half have a clear brand narrative in the form of a slogan. In addition, less than half exhibit some form of explicit co-branding, and where co-branding is evident, it is often limited to development agencies of the city or county council. Furthermore, most villages, towns and small islands lack a brand narrative and do not engage in co-branding. Accordingly, whilst destinations do have a website and a logo, there is a deficit with regard to brand narratives and co-branding

On the α−\alpha-decay of deformed actinide nuclei

$\alpha-$decay through a deformed potential barrier produces significant mixing of angular momenta when mapped from the nuclear interior to the outside. Using experimental branching ratios and either semi-classical or coupled-channels transmission matrices, we have found that there is a set of internal amplitudes which are essentially constant for all even--even actinide nuclei. These same amplitudes also give good results for the known anisotropic $\alpha-$particle emission of the favored decays of odd nuclei in the same mass region. PACS numbers: 23.60.+e, 24.10.Eq, 27.90.+bComment: 5 pages, latex (revtex style), 2 embedded postscript figures uuencoded gz-compressed .tar file To appear in Physical Review Letter

On the Rankin-Selberg integral of Kohnen and Skoruppa

The Rankin-Selberg integral of Kohnen and Skoruppa produces the Spin $L$-function for holomorphic Siegel modular forms of genus two. In this paper, we reinterpret and extend their integral to apply to arbitrary cuspidal automorphic representations of $\mathrm{PGSp}_4$. We show that the integral is related to a non-unique model and analyze it using the approach of Piatetski-Shapiro and Rallis.Comment: Final version. To appear in Math. Res. Let

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this paper, we show that using the Eigensystem Realization Algorithm (ERA) \citep{JuPa-85}, one can theoretically obtain exactly the same reduced order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure