The stability inequality for Ricci-flat cones

In this article, we thoroughly investigate the stability inequality for Ricci-flat cones. Perhaps most importantly, we prove that the Ricci-flat cone over CP^2 is stable, showing that the first stable non-flat Ricci-flat cone occurs in the smallest possible dimension. On the other hand, we prove that many other examples of Ricci-flat cones over 4-manifolds are unstable, and that Ricci-flat cones over products of Einstein manifolds and over Kähler-Einstein manifolds with h^{1,1}>1 are unstable in dimension less than 10. As results of independent interest, our computations indicate that the Page metric and the Chen-LeBrun-Weber metric are unstable Ricci shrinkers. As a final bonus, we give plenty of motivations, and partly confirm a conjecture of Tom Ilmanen relating the lambda-functional, the positive mass theorem and the nonuniqueness of Ricci flow with conical initial data

Impact of Patient Age on Postoperative Short-Term and Long-Term Outcome after Pancreatic Resection of Pancreatic Ductal Adenocarcinoma

(1) Purpose: to evaluate the impact of age on postoperative short-term and long-term outcomes in patients undergoing curative pancreatic resection for PDAC. (2) Methods: This retrospective single-center study comprised 213 patients who had undergone primary resection of PDAC from January 2000 to December 2018 at the University Hospital of Erlangen, Germany. Patients were stratified according the age into two groups: younger (≤70 years) and older (>70 years) patients. Postoperative outcome and long-term survival were compared between the groups. (3) Results: There were no significant differences regarding inhospital morbidity (58% vs. 67%, p = 0.255) or inhospital mortality (2% vs. 7%, p = 0.073) between the two groups. The median overall survival (OS) and disease-free survival (DFS) were significantly shorter in elderly patients (OS: 29.2 vs. 17.1 months, p < 0.001, respectively; DFS: 14.9 vs. 10.4 months, p = 0.034). Multivariate analysis revealed that age was a significant independent prognostic predictor for OS and DFS (HR 2.23, 95% CI 1.58–3.15; p < 0.001 for OS and HR 1.62, 95% CI 1.17–2.24; p = 0.004 for DFS). (4) Conclusion: patient age significantly influenced overall and disease-free survival in patients with PDAC undergoing primary resection in curative intent

Molecular Simulation of Olefin Oligomer Blend Phase Behavior

Configurational-bias Monte Carlo simulations in the Gibbs ensemble are used to study the thermodynamic and structural properties associated with the miscibility of binary olefin oligomer mixtures representing poly­(ethylene-<i>alt</i>-propylene), polypropylene, and head-to-head polypropylene. Single-component simulations are performed to compute the cohesive energy densities, Π_CED, of different oligomers that are often utilized in estimating the miscibilities of compounds in the liquid phase but are not measurable for high-boiling compounds, such as polymers. Extrapolating simulation data for C5 to C36 oligomers allows for determination of the infinite-chain-length Π_CED values of three polyolefins. The results agree remarkably well with values deduced from small-angle neutron scattering experiments on high-molecular-weight polymers. In addition, the Flory–Huggins χ parameters based on the free energy of mixing for pairs of olefins are calculated directly from simulations of binary mixtures. The binary propylene and head-to-head propylene oligomer blend is found to exhibit stabilized irregular mixing behavior, in agreement with its polymeric counterpart. This chain-length independence of the mixing behavior is interpreted via insights from structural analysis. Our results identify simulations of oligomeric systems as a promising route to predict and understand polymer blend phase behavior