On Periodic-Solutions of Certain nth Order Differential Equations

AbstractWe present two theorems on periodic solutions of nth-order ordinary differential equations with the right-hand side T-periodic with respect to the time variable. We apply a topological method based on the Lefschetz Fixed Point Theorem and the Wazewski Principle

Contemporary Presentation and Management of Valvular Heart Disease The EURObservational Research Programme Valvular Heart Disease II Survey

International audienceBackground: Valvular heart disease (VHD) is an important cause of mortality and morbidity and has been subject to important changes in management. The VHD II survey was designed by the EURObservational Research Programme of the European Society of Cardiology to analyze actual management of VHD and to compare practice with guidelines. Methods: Patients with severe native VHD or previous valvular intervention were enrolled prospectively across 28 countries over a 3-month period in 2017. Indications for intervention were considered concordant if the intervention was performed or scheduled in symptomatic patients, corresponding to Class I recommendations specified in the 2012 European Society of Cardiology and in the 2014 American Heart Association/American College of Cardiology VHD guidelines. Results: A total of 7247 patients (4483 hospitalized, 2764 outpatients) were included in 222 centers. Median age was 71 years (interquartile range, 62-80 years); 1917 patients (26.5%) were >= 80 years; and 3416 were female (47.1%). Severe native VHD was present in 5219 patients (72.0%): aortic stenosis in 2152 (41.2% of native VHD), aortic regurgitation in 279 (5.3%), mitral stenosis in 234 (4.5%), mitral regurgitation in 1114 (21.3%; primary in 746 and secondary in 368), multiple left-sided VHD in 1297 (24.9%), and right-sided VHD in 143 (2.7%). Two thousand twenty-eight patients (28.0%) had undergone previous valvular intervention. Intervention was performed in 37.0% and scheduled in 26.8% of patients with native VHD. The decision for intervention was concordant with Class I recommendations in symptomatic patients with severe single left-sided native VHD in 79.4% (95% CI, 77.1-81.6) for aortic stenosis, 77.6% (95% CI, 69.9-84.0) for aortic regurgitation, 68.5% (95% CI, 60.8-75.4) for mitral stenosis, and 71.0% (95% CI, 66.4-75.3) for primary mitral regurgitation. Valvular interventions were performed in 2150 patients during the survey; of them, 47.8% of patients with single left-sided native VHD were in New York Heart Association class III or IV. Transcatheter procedures were performed in 38.7% of patients with aortic stenosis and 16.7% of those with mitral regurgitation. Conclusions: Despite good concordance between Class I recommendations and practice in patients with aortic VHD, the suboptimal number in mitral VHD and late referral for valvular interventions suggest the need to improve further guideline implementation