A 2D-variant of a theorem of Uraltseva and Urdaletova for higher order variational problems

If \Omega is a domain in \mathbb{R}^{2} and if u:\Omega\rightarrow\mathbb{R} locally minimizes the energy \int_{\Omega}\left[h_{1}(\left|(\nabla^{2}u)_{I}\right|)+h_{2}(\left|(\nabla^{2}u)_{II}\right|)\right]dx, where (\nabla^{2}u)_{I}, (\nabla^{2}u)_{II} denotes a decomposition of the Hessian matrix \nabla^{2}u, then we prove the higher integrability and even the continuity of \nabla^{2}u under rather general assumptions imposed on the N-functions h_{1}, h_{2}

Existence of global solutions for a parabolic system related to the nonlinear Stokes problem

In this note we consider an initial-boundary value problem describing a nonlinear variant of the nonstationary Stokes equation. We prove the existence of a (unique) global solution with Galerkin-type arguments

Importance of Status Quo When Lobbying a Coalition Government

Lobbying a coalition government is different from lobbying a single-party government, since in the case of a coalition government, the interest group can intervene in the intragovernmental decision process. In the case where the interest group prefers the status quo to the surplus maximizing policy, the interest group influences the policy without any contribution due to its credible threat to block unfavorable proposals. Furthermore, we show that when, say, a leftist coalition government may be replaced by a rightist coalition government, the final policy reflects a rightist interest group's preferences more heavily due to the interest group's forward-looking considerations.</p

Interior gradient bounds for local minimizers of variational integrals under nonstandard growth conditions

Inspired by the work of Marcellini and Papi [MP] we consider local minima u:&#92;mathbb{R}^{n}&#92;supset&#92;Omega&#92;rightarrow&#92;mathbb{R}^{M} of variational integrals of the form &#92;int_{&#92;Omega}h(&#92;left|&#92;nabla u&#92;right|)dx and prove interior gradient bounds under rather general assumptions on h working with the additional hypothesis that u is locally bounded. Our requirements imposed on the density h do not involve the dimension n

On local generalized minimizers and local stress tensors for variational problems with linear growth

Uniqueness and regularity results for local vector-valued generalized minimizers and for local stress tensors associated to variational problems with linear growth conditions are established. Assuming that the energy density f has the structure f(Z)=h(|Z|), only very weak ellipticity assumptions are required. For the proof we combine arguments from measure theory and convex analysis with the regularity results of [ABF]

Protocol for a prospective double-blind, randomised, placebo-controlled feasibility trial of octreotide infusion during liver transplantation

Introduction Liver transplantation is a complex operation that can provide significant improvements in quality of life and survival to the recipients. However, serious complications are common and include major haemorrhage, hypotension and renal failure. Blood transfusion and the development of acute kidney injury lead to both short-term and long-term poor patient outcomes, including an increased risk of death, graft failure, length of stay and reduced quality of life. Octreotide may reduce the incidence of renal dysfunction, perioperative haemorrhage and enhance intraoperative blood pressure. However, octreotide does have risks, including resistant bradycardia, hyperglycaemia and hypoglycaemia and QT prolongation. Hence, a randomised controlled trial of octreotide during liver transplantation is needed to determine the cost-efficacy and safety of its use; this study represents a feasibility study prior to this trial. Methods and analysis We describe a multicentre, double-blind, randomised, placebo-controlled feasibility study of continuous infusion of octreotide during liver transplantation surgery. We will recruit 30 adult patients at two liver transplant centres. A blinded infusion during surgery will be administered in a 2:1 ratio of octreotide:placebo. The primary outcomes will determine the feasibility of this study design. These include the recruitment ratio, correct administration of blinded study intervention, adverse event rates, patient and clinician enrolment refusal and completion of data collection. Secondary outcome measures of efficacy and safety will help shape future trials by assessing potential primary outcome measures and monitoring safety end points. No formal statistical tests are planned. This manuscript represents study protocol number 1.3, dated 2 June 2021. Ethics and dissemination This study has received Research Ethics Committee approval. The main study outcomes will be submitted to an open-access journal. Trial sponsor The Joint Research Office, University College London, UK. Neither the sponsor nor the funder have any role in study design, collection, management, analysis and interpretation of data, writing of the study report or the decision to submit the report for publication. Trial registration The study is registered with ClinicalTrials.gov (NCT04941911) with recruitment due to start in August 2021 with anticipated completion in July 2022. Clinical trials unit Surgical and Interventional Group, Division of Surgery & Interventional Science, University College London

Weapon injuries in the crusader mass graves from a 13th century attack on the port city of Sidon (Lebanon).

Archaeological excavations close to St Louis' castle in Sidon, Lebanon have revealed two mass grave deposits containing partially articulated and disarticulated human skeletal remains. A minimum of 25 male individuals have been recovered, with no females or young children. Radiocarbon dating of the human remains, a crusader coin, and the design of Frankish belt buckles strongly indicate they belong to a single event in the mid-13th century CE. The skeletal remains demonstrate a high prevalence of unhealed sharp force, penetrating force and blunt force trauma consistent with medieval weaponry. Higher numbers of wounds on the back of individuals than the front suggests some were attacked from behind, possibly as they fled. The concentration of blade wounds to the back of the neck of others would be compatible with execution by decapitation following their capture. Taphonomic changes indicate the skeletal remains were left exposed for some weeks prior to being collected together and re-deposited in the defensive ditch by a fortified gateway within the town wall. Charring on some bones provides evidence of burning of the bodies. The findings imply the systematic clearance of partially decomposed corpses following an attack on the city, where adult and teenage males died as a result of weapon related trauma. The skeletons date from the second half of the Crusader period, when Christian-held Sidon came under direct assault from both the Mamluk Sultanate (1253 CE) and the Ilkhanate Mongols (1260 CE). It is likely that those in the mass graves died during one of these assaults

Heat transport in insulators from ab initio Green-Kubo theory

The Green-Kubo theory of thermal transport has long be considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at the quantum-mechanical level. Besides, experience with classical simulations indicates that the estimate of heat-transport coefficients requires analysing molecular trajectories that are more than one order of magnitude longer than deemed feasible using ab initio molecular dynamics. In this paper we report on recent theoretical advances that are allowing one to overcome these two obstacles. First, a general gauge invariance principle has been established, stating that thermal conductivity is insensitive to many details of the microscopic expression for the energy density and current from which it is derived, thus permitting to establish a rigorous expression for the energy flux from Density-Functional Theory, from which the conductivity can be computed in practice. Second, a novel data analysis method based on the statistical theory of time series has been proposed, which allows one to considerably reduce the simulation time required to achieve a target accuracy on the computed conductivity. These concepts are illustrated in detail, starting from a pedagogical introduction to the Green-Kubo theory of linear response and transport, and demonstrated with a few applications done with both classical and quantum-mechanical simulation methods.Comment: 36 pages, 14 figure