4,743 research outputs found

    Corona-type theorems and division in some function algebras on planar domains

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    Let AA be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if f,f1,,fnAf,f_1,\dots,f_n\in A satisfy fj=1nfj|f|\leq \sum_{j=1}^n |f_j|, does there exist gjAg_j\in A and a constant NNN\in\N such that fN=j=1ngjfjf^N=\sum_{j=1}^n g_j f_j? A prominent role in our proofs is played by a new space, C_{\dbar, 1}(K), which we call the algebra of \dbar-smooth functions. In the case n=1n=1, a complete solution is given for the algebras Am(K)A^m(K) of functions holomorphic in KK^\circ and whose first mm-derivatives extend continuously to \ov{K^\circ}. This necessitates the introduction of a special class of compacta, the so-called locally L-connected sets. We also present another constructive proof of the Nullstellensatz for A(K)A(K), that is only based on elementary \dbar-calculus and Wolff's method.Comment: 23 pages, 6 figure

    Final Report: Talking about sex and relationships: The views of young people with learning disabilities

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    We ran a drama group with young people with learning disabilities. We also interviewed parents of young people with learning disabilities. We also talked to groups of teachers. There has not been much research done about this before

    Identification of behaviour change techniques and engagement strategies to design a smartphone app to reduce alcohol consumption using a formal consensus method

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    Background: Digital interventions to reduce excessive alcohol consumption have the potential to have a broader reach and be more cost-effective than traditional brief interventions. However, there is not yet a strong evidence base on their ability to engage users or on their effectiveness. Objective: This study aimed to identify the behaviour change techniques (BCTs) and engagement strategies most worthy of further study by inclusion in a smartphone application (app) to reduce alcohol consumption, using formal expert consensus methods. Methods: The first phase of the study consisted of a Delphi exercise with three rounds. It was conducted with seven international experts in the field of alcohol and/or behaviour change. In the first round, experts identified BCTs most likely to be effective at reducing alcohol consumption and strategies most likely to engage users with an app; these were rated in the second round; and those rated as effective by at least four out of seven participants were ranked in the third round. The rankings were analysed using Kendall’s W coefficient of concordance, which indicates consensus between participants. The second phase consisted of a new, independent group of experts (n=43) ranking the BCTs that were identified in the first phase. The correlation between the rankings of the two groups was assessed using Spearman’s rank correlation coefficient. Results: Twelve BCTs were identified as likely to be effective. There was moderate agreement among the experts over their ranking (W=.465, χ2(11)=35.77, P<.001) and the BCTs receiving the highest mean rankings were self-monitoring, goal-setting, action planning, and feedback in relation to goals. There was a significant correlation between the ranking of the BCTs by the group of experts who identified them and a second independent group of experts (Spearman’s rho=.690, P=.01). Seventeen responses were generated for strategies likely to engage users. There was moderate agreement among experts on the ranking of these engagement strategies (W=.563, χ2(15)=59.16, P<.001) and those with the highest mean rankings were ease of use, design – aesthetic, feedback, function, design – ability to change design to suit own preferences, tailored information, and unique smartphone features. Conclusions: The BCTs with greatest potential to include in a smartphone app to reduce alcohol consumption were judged by experts to be self-monitoring, goal-setting, action planning, and feedback in relation to goals. The strategies most likely to engage users were ease of use, design, tailoring of design and information, and unique smartphone features

    The Mid-infrared Fine-structure Lines of Neon as an Indicator of Star For mation Rate in Galaxies

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    The fine-structure lines of singly ([Ne II] 12.8 micron) and doubly ([Ne III] 15.6 micron) ionized neon are among the most prominent features in the mid-infrared spectra of star-forming regions, and have the potential to be a powerful new indicator of the star formation rate in galaxies. Using a sample of star-forming galaxies with measurements of the fine-structure lines available from the literature, we show that the sum of the [Ne II] and [Ne III] luminosities obeys a tight, linear correlation with the total infrared luminosity, over 5 orders of magnitude in luminosity. We discuss the formation of the lines and their relation with the Lyman continuum luminosity. A simple calibration between star formation rate and the [Ne II]+[Ne III] luminosity is presented.Comment: To appear in ApJ. 8 page
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