Bott‐integrable Reeb flows on 3‐manifolds Geiges, Hansjörg; Hedicke, Jakob; Sağlam, Murat
Journal of the London Mathematical Society,
January 2024, 2024-01-00, Letnik:
109, Številka:
1
Journal Article
Recenzirano
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This paper is devoted to studying a notion of Bott integrability for Reeb flows on contact 3‐manifolds. We show, in analogy with work of Fomenko–Zieschang on Hamiltonian flows in dimension 4, that ...Bott‐integrable Reeb flows exist precisely on graph manifolds. We also show that all S1$S^1$‐invariant contact structures on Seifert manifolds, as well as all contact structures on the 3‐sphere, on the 3‐torus and on S1×S2$S^1\times S^2$, admit Bott‐integrable Reeb flows. Along the way, we establish some general Liouville‐type theorems for Bott‐integrable Reeb flows, and a number of topological constructions (connected sum, open books, Dehn surgery) that may be expected to have wider applications.
Forgings are produced in several process steps, the so-called forging sequence. The design of efficient forging sequences is a very complex and iterative development process. In order to automate ...this process and to reduce the development time, a method is presented here, which automatically generates multi-stage forging sequences for different forging geometries on the basis of the component geometry (STL file). The method was developed for closed die forging. The individual modules of this forging sequence design method (FSD method) as well as the functioning of the algorithm for the generation of the intermediate forms are presented. The method is applied to different forgings with different geometrical characteristics. The generated forging sequences are checked with FE simulations for the quality criteria form filling and freedom from folds. The simulation results show that the developed FSD method provides good approximate solutions for an initial design of forging sequences for closed die forging in a short time.
Postoperative arrhythmias (PAs) are common events and have been widely investigated in cardiothoracic surgery. Within visceral surgery, a recent study revealed a significant occurrence of PA in ...esophageal resections. In contrast, PA in lower gastrointestinal surgery is rarely investigated and has been rudimentary described in the medical literature. The present work is a retrospective cohort study of 1171 patients who underwent surgery of lower gastrointestinal tract between 2012 and 2018. All included patients were treated and monitored in the intensive care unit (ICU) or intermediate care unit (IMC) after surgery. Follow-up, performed between January and May 2021, was obtained for the patients with PA investigating the possible persistence of PA and complications such as permanent arrhythmia or thromboembolic events after discharge. In total, n = 1171 patients (559 female, 612 male) without any history of prior arrhythmia were analyzed. Overall, PA occurred in n = 56 (4.8%) patients after surgery of the lower GI. The highest incidence of PA was seen in patients undergoing bowel surgery after mesenteric ischaemia (26.92%), followed by cytoreductive surgery (CRS) combined with hyperthermic intraperitoneal chemotherapy (HIPEC; 16.67%). PA was significantly associated with higher age (72 years (IQR 63-78 years) vs. 64 years (IQR 55-73.5 years), p < 0.001) and longer length of stay in the ICU (median 15 days (IQR 5-25 days) vs. median 2 days (IQR 1-5 days), p < 0.001). PA was independently associated with organ failure (OR = 4.62, 95% CI 2.11-10.11, p < 0.001) and higher in-house mortality (OR = 3.37, 95% CI 1.23-9.28, p < 0.001). In median, PA occurred 66.5 h after surgery. In follow-up, 31% of all the patients with PA showed development of permanent arrhythmia. The incidence of PA after lower GI surgery is comparatively low. Its occurrence, however, seems to have severe implications since it is significantly associated with higher rates of organ failure and in-house mortality. Also, compared to the general population, the development of permanent arrhythmia is significantly higher in patients who developed new-onset PA.
The influence of counterions and co-ions on the stability and thickness of foam films stabilized by anionic dodecyl sulfate (DS−) has been studied in a thin film pressure balance. Particularly, the ...effect on the properties of foam films of (i) the counterions Li+, Na+, and Cs+ of DS− and (ii) monovalent inorganic salts added to sodium dodecyl sulfate solutions is considered. Generally, addition of salt improved the stability of the foam films. As a second order, an increasing ionic size led to an increased adsorption, which in the case of cations gave thinner and less stable films and in the case of anions led to thicker and more stable films. Hence, an effect of anions was observed though the film surfaces were already negatively charged by the anionic DS−, leading to the conclusion that adsorption of anions to the film surface is governed by ion specific rather than electrostatic interactions. At a fixed surfactant and varying salt concentration, a maximum in film thickness could be identified at a salt concentration well below the surfactant concentration. We anticipate that (i) at low salt concentration salt mainly affects the charging of a film interface, whereas (ii) at high salt concentration salt mainly affects the screening of the electrostatic repulsion between the two interfaces of the film.
New-onset postoperative arrhythmia (PA) has previously been described as a pivotal risk factor for postoperative morbidity and mortality after visceral surgery. However, there is a lack of data ...concerning liver surgery. The incidence and impact of new-onset postoperative arrhythmia after liver surgery was, therefore, analyzed in a monocentric study.
In total,
= 460 patients (221 female, 239 male) who underwent liver surgery between January 2012 and April 2020 without any prior arrhythmia in their medical history were included in this retrospective analysis. Clinical monitoring started with the induction of anesthesia and was terminated with discharge from the intensive care unit (ICU) or intermediate care unit (IMC). Follow-up included documentation of complications during the hospital stay, as well as long-term survival analysis.
Postoperative arrhythmia after liver surgery was observed in 25 patients, corresponding to an incidence of 5.4%. The occurrence of arrhythmia was significantly associated with intraoperative complications (
< 0.05), liver fibrosis/cirrhosis (
< 0.05), bile fistula/bile leakage/bilioma (
< 0.05), and organ failure (
< 0.01). Survival analysis showed a significantly poorer overall survival of patients who developed postoperative arrhythmia after liver surgery (
< 0.001).
New-onset postoperative arrhythmia after liver surgery has an incidence of only 5.4% but is significantly associated with higher postoperative morbidity and poorer overall survival.
We show that the natural conjugation invariant cone structure on the linear
symplectic group $\mathrm{Sp}(2n)$ is globally hyperbolic in the positively
elliptic region ...$\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$. This answers a question
by Abbondandolo, Benedetti and Polterovich and shows a formula for a
bi-invariant Lorentzian distance function dened by these authors for elements
in this region. Moreover we give a characterisation of the positively elliptic
region and of $-id \in\mathrm{Sp}(2n)$ in terms of the causality of this cone
structure.
Summary Objectives In Germany the estimation of a population based annual incidence of community acquired pneumonia (CAP) in adults has been referred to the denominator problem. To estimate a ...population based annual incidence of CAP in an urban German area we compared the incidence estimated on four different approaches. Methods We estimated the annual incidence on the basis of the covered population of sentinel practices from Luebeck participating in the German competence network CAPNETZ. We estimated the incidence on the basis of a population based survey, on the basis of the mortality and lethality in Luebeck, and on the basis of data of the regional Association of Statutory Health Insurance Physicians (“Kassenärztliche Vereinigung (KV) Schleswig-Holstein”). Results The annual incidence of CAP in Luebeck was 3.7/1000 inhabitants (95% confidence interval (CI) 2.4–5.5), 6.0/1000 inhabitants, 8.7/1000 inhabitants (95% CI 8.2–9.1), or 10.1/1000 inhabitants (95% CI 9.6–10.5) depending on the approach of estimation. According to this, in Germany we would expect 400,000–680,000 new CAP cases per year. Conclusions The true incidence of CAP in Luebeck might range between 3.7 and 10 per 1000 inhabitants. Comparisons with the rates in the literature are difficult due to the differences in the applied methods.
We define a Lorentzian distance function on the group of contactomorphisms of a closed contact manifold. This distance function is continuous with respect to the Hofer norm on the group of ...contactomorphisms defined by Shelukhin and finite if and only if the group of contactomorphisms is orderable. To prove this we show that intervals defined by the positivity relation are open with respect to the topology induced by the Hofer norm. For orderable Legendrian isotopy classes we show that the Chekanov-type metric defined by Rosen and Zhang is non-degenerate. In this case similar results hold for a Lorentzian distance function on Legendrian isotopy classes. This leads to a natural class of metrics associated to a globally hyperbolic Lorentzian manifold such that its Cauchy hypersurface has a unit co-tangent bundle with orderable isotopy class of the fibres.
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