Inflectional loci of scrolls

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let \L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of \L are locally free. The inflectional loci of $X$ can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas imply that the only uninflected scrolls are the balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif

Efficacy of labral repair, biceps tenodesis, and diagnostic arthroscopy for SLAP Lesions of the shoulder: a randomised controlled trial

<p>Abstract</p> <p>Background</p> <p>Surgery for type II SLAP (superior labral anterior posterior) lesions of the shoulder is a promising but unproven treatment. The procedures include labral repair or biceps tenodesis. Retrospective cohort studies have suggested that the benefits of tenodesis include pain relief and improved function, and higher patient satisfaction, which was reported in a prospective non-randomised study. There have been no completed randomised controlled trials of surgery for type II SLAP lesions. The aims of this participant and observer blinded randomised placebo-controlled trial are to compare the short-term (6 months) and long-term (2 years) efficacy of labral repair, biceps tenodesis, and placebo (diagnostic arthroscopy) for alleviating pain and improving function for type II SLAP lesions.</p> <p>Methods/Design</p> <p>A double-blind randomised controlled trial are performed using 120 patients, aged 18 to 60 years, with a history for type II SLAP lesions and clinical signs suggesting type II SLAP lesion, which were documented by MR arthrography and arthroscopy. Exclusion criteria include patients who have previously undergone operations for SLAP lesions or recurrent shoulder dislocations, and ruptures of the rotator cuff or biceps tendon. Outcomes will be assessed at baseline, three, six, 12, and 24 months. Primary outcome measures will be the clinical Rowe Score (1988-version) and the Western Ontario Instability Index (WOSI) at six and 24 months. Secondary outcome measures will include the Shoulder Instability Questionnaire (SIQ), the generic EuroQol (EQ-5 D and EQ-VAS), return to work and previous sports activity, complications, and the number of reoperations.</p> <p>Discussion</p> <p>The results of this trial will be of international importance and the results will be translatable into clinical practice.</p> <p>Trial Registration</p> <p><b>[ClinicalTrials.gov NCT00586742]</b></p