Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \cite{BKD}, a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic

A macro-modelling approach for the analysis of infilled frame structures considering the effects of openings and vertical loads

During the last decades, several macro-models have been proposed for the modelling of the infill panels' contribution to the lateral strength of frames. Despite all this effort, a robust model, which takes into account the influence of the vertical load, is not yet available. Furthermore, the influence of the very common case of infill walls with openings, such as windows and doors, has been neglected in all the code provisions that have been published so far. In this paper, an updated macro-model, based on the equivalent pin-jointed diagonal compressive strut, is presented. The proposed macro-model is able to represent the stiffening effect of the infill panel with openings by taking into account both the size of the opening and the vertical load acting on the frame. Detailed and in-depth parametrical investigation, based on finite element analysis, shows that the proposed mathematical macro-model can be used as a reliable and useful tool for the determination of the equivalent compressive strut width since it accounts for a large number of parameters, which are not generally accounted for by the already available models in the literature

Body mass index and complications following major gastrointestinal surgery: A prospective, international cohort study and meta-analysis

Aim Previous studies reported conflicting evidence on the effects of obesity on outcomes after gastrointestinal surgery. The aims of this study were to explore the relationship of obesity with major postoperative complications in an international cohort and to present a metaanalysis of all available prospective data. Methods This prospective, multicentre study included adults undergoing both elective and emergency gastrointestinal resection, reversal of stoma or formation of stoma. The primary end-point was 30-day major complications (Clavien–Dindo Grades III–V). A systematic search was undertaken for studies assessing the relationship between obesity and major complications after gastrointestinal surgery. Individual patient meta-analysis was used to analyse pooled results. Results This study included 2519 patients across 127 centres, of whom 560 (22.2%) were obese. Unadjusted major complication rates were lower in obese vs normal weight patients (13.0% vs 16.2%, respectively), but this did not reach statistical significance (P = 0.863) on multivariate analysis for patients having surgery for either malignant or benign conditions. Individual patient meta-analysis demonstrated that obese patients undergoing surgery formalignancy were at increased risk of major complications (OR 2.10, 95% CI 1.49–2.96, P < 0.001), whereas obese patients undergoing surgery for benign indications were at decreased risk (OR 0.59, 95% CI 0.46–0.75, P < 0.001) compared to normal weight patients. Conclusions In our international data, obesity was not found to be associated with major complications following gastrointestinal surgery. Meta-analysis of available prospective data made a novel finding of obesity being associated with different outcomes depending on whether patients were undergoing surgery for benign or malignant disease