Spherical harmonics and integration in superspace

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

Incidence of Atrial Fibrillation in Patients with either Heart Failure or Acute Myocardial Infarction and Left Ventricular Dysfunction: A Cohort Study

<p>Abstract</p> <p>Background</p> <p>We examined the incidence of new-onset atrial fibrillation in patients with left ventricular dysfunction. Patients either had a recent myocardial infarction (with or without clinical heart failure) or symptomatic heart failure (without a recent MI). Patients were with and without treatment with the class III antiarrhythmic drug dofetilide over 36 months.</p> <p>Methods</p> <p>The Danish Investigations of Arrhythmia and Mortality ON Dofetilide (DIAMOND) studies included 2627 patients without atrial fibrillation at baseline, who were randomised to treatment with either dofetilide or placebo.</p> <p>Results</p> <p>The competing risk analyses estimated the cumulative incidences of atrial fibrillation during the 42 months of follow-up to be 9.6% in the placebo-treated heart failure-group, and 2.9% in the placebo-treated myocardial infarction-group.</p> <p>Cox proportional hazard regression found a 42% significant reduction in the incidence of new-onset AF when assigned to dofetilide compared to placebo (hazard ratio 0.58, 95% confidence interval 0.40-0.82) and there was no interaction with study (p = 0.89).</p> <p>In the heart failure-group, the incidence of atrial fibrillation was significantly reduced to 5.6% in the dofetilide-treated patients (hazard ratio 0.57, 95% confidence interval 0.38-0.86).</p> <p>In the myocardial infarction-group the incidence of atrial fibrillation was reduced to 1.7% with the administration of dofetilide. This reduction was however not significant (hazard ratio 0.61, 95% confidence interval 0.30-1.24).</p> <p>Conclusion</p> <p>In patients with left ventricular dysfunction the incidence of AF in 42 months was 9.6% in patients with heart failure and 2.9% in patients with a recent MI. Dofetilide significantly reduced the risk of developing atrial fibrillation compared to placebo in the entire study group and in the subgroup of patients with heart failure. The reduction in the subgroup with recent MI was not statistically significant, but the hazard ratio was similar to the hazard ratio for the heart failure patients, and there was no difference between the effect in the two studies (p = 0.89 for interaction).</p

Socioeconomic determinants of psychotropic drug utilisation among elderly: a national population-based cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Psychotropic drugs are commonly utilised among the elderly. This study aimed to analyse whether two socioeconomic determinants - income and marital status - are associated with differences in utilisation of psychotropic drugs and potentially inappropriate psychotropic drugs among elderly in Sweden.</p> <p>Methods</p> <p>All individuals aged 75 years and older who had purchased a psychotropic drug in Sweden during 2006 were included (68.7% women, n = 384712). Data was collected from national individual-based registers. Outcome measures were utilisation of three or more psychotropic drugs and utilisation of potentially inappropriate psychotropic drugs, as classified by the Swedish National Board of Health and Welfare.</p> <p>Results</p> <p>Individuals with low income were more likely to utilise three or more psychotropic drugs compared to those with high income; adjusted odds ratio (aOR) 1.12 (95% confidence interval [CI] 1.10-1.14). The non-married had a higher probability for utilising three or more psychotropic drugs compared to the married (aOR 1.22; CI 1.20-1.25). The highest probability was observed among the divorced and the never married. Potentially inappropriate psychotropic drugs were more common among individuals with low compared to high income (aOR 1.14; CI 1.13-1.16). Compared to the married, potentially inappropriate psychotropic drug utilisation occurred more commonly among the non-married (aOR 1.08; CI 1.06-1.10). The never married and the divorced had the highest probability.</p> <p>Conclusions</p> <p>There was an association between socioeconomic determinants and psychotropic drug utilisation. The probability for utilising potentially inappropriate psychotropics was higher among individuals with low income and among the non-married.</p

Postoperative complications after procedure for prolapsed hemorrhoids (PPH) and stapled transanal rectal resection (STARR) procedures

Procedure for prolapsing hemorrhoids (PPH) and stapled transanal rectal resection for obstructed defecation (STARR) carry low postoperative pain, but may be followed by unusual and severe postoperative complications. This review deals with the pathogenesis, prevention and treatment of adverse events that may occasionally be life threatening. PPH and STARR carry the expected morbidity following anorectal surgery, such as bleeding, strictures and fecal incontinence. Complications that are particular to these stapled procedures are rectovaginal fistula, chronic proctalgia, total rectal obliteration, rectal wall hematoma and perforation with pelvic sepsis often requiring a diverting stoma. A higher complication rate and worse results are expected after PPH for fourth-degree piles. Enterocele and anismus are contraindications to PPH and STARR and both operations should be used with caution in patients with weak sphincters. In conclusion, complications after PPH and STARR are not infrequent and may be difficult to manage. However, if performed in selected cases by skilled specialists aware of the risks and associated diseases, some complications may be prevented