Covers of acts over monoids II

In 1981 Edgar Enochs conjectured that every module has a flat cover and finally proved this in 2001. Since then a great deal of effort has been spent on studying different types of covers, for example injective and torsion free covers. In 2008, Mahmoudi and Renshaw initiated the study of flat covers of acts over monoids but their definition of cover was slightly different from that of Enochs. Recently, Bailey and Renshaw produced some preliminary results on the `other' type of cover and it is this work that is extended in this paper. We consider free, divisible, torsion free and injective covers and demonstrate that in some cases the results are quite different from the module case

Exploring Tai Chi in rheumatoid arthritis: a quantitative and qualitative study

<p>Abstract</p> <p>Background</p> <p>Rheumatoid arthritis (RA) is a chronic, inflammatory and systemic disease which affects the musculoskeletal system. Exercise programmes are reported to improve physical functioning in patients with RA. Tai Chi is a traditional Chinese martial art which combines slow and gentle movements with mental focus. The purpose of this study was to study in which way Tai Chi group exercise impacted on disease activity, physical function, health status and experience in RA patients, applying quantitative and qualitative methods.</p> <p>Methods</p> <p>Fifteen patients with RA (13 females, age 33-70 years) were recruited from a rheumatology department into a single group study. The patients were instructed in Tai Chi exercise twice weekly for 12 weeks. Assessments at baseline, 12 weeks, and 12 weeks follow-up were performed with a wide range of measures, including disease activity, self-reported health status, physical performance tests (Walking in Figure of Eight, Timed-Stands Test, and Shoulder Movement Impairment Scale). Qualitative data were obtained from a focus group interview conducted after completed intervention with taping and verbatim transcription. Review of the transcripts identified themes important to patients practicing Tai Chi.</p> <p>Results</p> <p>Within the group, Tai Chi practice lead to improved lower-limb muscle function at the end of intervention and at 12 weeks follow-up. Qualitative analyses showed that patients experienced improved physical condition, confidence in moving, balance and less pain during exercise and in daily life. Other experience included stress reduction, increased body awareness, confidence in moving and indicated that Tai Chi was a feasible exercise modality in RA.</p> <p>Conclusions</p> <p>Improved muscle function in lower limbs was also reflected when patient experiences with Tai Chi were studied in depth in this explorative study. The combination of qualitative and quantitative research methods shows that Tai Chi has beneficial effects on health not related to disease activity and standardised health status assessment, and may contribute to an understanding of how Tai Chi exerts its effects.</p> <p>Trial registration</p> <p>NCT00522054</p

A Q-methodology study of flare help-seeking behaviours and different experiences of daily life in rheumatoid arthritis

© 2014 Lin et al.; licensee BioMed Central Ltd. Background: Previous studies have not addressed rheumatoid arthritis (RA) patients' help-seeking behaviours for RA flares, and only one small qualitative study has addressed how patients experience daily life on current treatment regimes. Thus, this study aims to identify clusters of opinion related to RA patients' experiences of daily life on current treatments, and their help-seeking behaviours for RA flares. Methods: Using Q-methodology (a methodology using qualitative and quantitative methods to sort people according to subjective experience), two separate studies were conducted with the same sample of RA patients (mean age 55, 73% female). Thirty participants sorted 39 statements about daily life (Q-study 1) and 29 participants separately sorted 23 statements about flare help-seeking (Q-study 2). Data were examined using Q-factor analysis. Results: Daily life with RA (Q-study 1): Three factors relating to the experience of living with RA were extracted and explained. Patients belonging to Factor A (mean age 62, 86% female) use effective self-management techniques to control the daily impact of RA. Those in Factor B (mean age 55, 75% male) struggle to self-manage and cope. Whilst patients in Factor C (mean age 42, 100% female) prioritise life responsibilities over their RA, reporting less impact. Flare help-seeking (Q-study 2): Two factors explaining the experience of flare help-seeking (unrelated to the factors from Q-study 1) were extracted and explained. Factor X (68.8% on biologics) reported seeking help quickly, believing the medical team is there to help. Factor Y (0% on biologics) delay help-seeking, concerned about wasting the rheumatologist's time, believing they should manage alone. All participants agreed they sought help due to intense pain and persistent, unmanageable symptoms. Conclusions: Patients with different characteristics appear to manage RA life in different ways and men may struggle more than women. Whilst all patients are prompted to seek help by persistent, unmanageable symptoms, some delay help-seeking. Further research is needed to quantify the severity of daily symptoms, the level of symptoms needed for patients to define themselves as in flare and to understand the support needs of RA men

Reproductive Ecology and Severe Pollen Limitation in the Polychromic Tundra Plant, Parrya nudicaulis (Brassicaceae)

Pollen limitation is predicted to be particularly severe in tundra habitats. Numerous reproductive patterns associated with alpine and arctic species, particularly mechanisms associated with reproductive assurance, are suggested to be driven by high levels of pollen limitation. We studied the reproductive ecology of Parrya nudicaulis, a species with relatively large sexual reproductive investment and a wide range of floral pigmentation, in tundra habitats in interior montane Alaska to estimate the degree of pollen limitation. The plants are self-compatible and strongly protandrous, setting almost no seed in the absence of pollinators. Supplemental hand pollinations within pollinator exclusion cages indicated no cage effect on seed production. Floral visitation rates were low in both years of study and particularly infrequent in 2010. A diversity of insects visited P. nudicaulis, though syrphid and muscid flies composed the majority of all visits. Pollen-ovule ratios and levels of heterozygosity are consistent with a mixed mating system. Pollen limitation was severe; hand pollinations increased seed production per plant five-fold. Seed-to-ovule ratios remained low following hand pollinations, indicating resource limitation is likely to also be responsible for curtailing seed set. We suggest that pollen limitation in P. nudicaulis may be the result of selection favoring an overproduction of ovules as a bet-hedging strategy in this environmental context of highly variable pollen receipt

Transitional Care for Patients with Congenital Colorectal Diseases: An EUPSA Network Office, ERNICA, and eUROGEN Joint Venture

Background: Transition of care (TOC; from childhood into adulthood) of patients with anorectal malformations (ARM) and Hirschsprung disease (HD) ensures continuation of care for these patients. The aim of this international study was to assess the current status of TOC and adult care (AC) programs for patients with ARM and HD. Methods: A survey was developed by members of EUPSA, ERN eUROGEN, and ERNICA, including patient representatives (ePAGs), comprising of four domains: general information, general questions about transition to adulthood, and disease-specific questions regarding TOC and AC programs. Recruitment of centres was done by the ERNs and EUPSA, using mailing lists and social media accounts. Only descriptive statistics were reported. Results: In total, 82 centres from 21 different countries entered the survey. Approximately half of them were ERN network members. Seventy-two centres (87.8%) had a self-reported area of expertise for both ARM and HD. Specific TOC programs were installed in 44% of the centres and AC programs in 31% of these centres. When comparing centres, wide variation was observed in the content of the programs. Conclusion: Despite the awareness of the importance of TOC and AC programs, these programs were installed in less than 50% of the participating centres. Various transition and AC programs were applied, with considerable heterogeneity in implementation, content and responsible caregivers involved. Sharing best practice examples and taking into account local and National Health Care Programs might lead to a better continuation of care in the future. Level of Evidence: III

The Future of Rheumatoid Arthritis and Hand Surgery - Combining Evolutionary Pharmacology and Surgical Technique

Rheumatoid arthritis is a systemic autoimmune disease of uncertain aetiology, which is characterized primarily by synovial inflammation with secondary skeletal destructions

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function