Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

This paper deals with the eigenvalue problem for the operator $L=-\Delta -x\cdot \nabla$ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue $\lambda_k$ of $L$ under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any $c>0$ and $k\in \mathbb{N}$ the following minimization problem \min\left\{\lambda_k(\Omega): \> \Omega \>\mbox{quasi-open} \>\mbox{set}, \> \int_\Omega e^{|x|^2/2}dx\le c\right\} has a solution

A note on the Serrin problem in the plane

We investigate the stability of the radial symmetry for the overdetermined Serrin problem in a planar convex set. More precisely, we prove that, whenever we properly perturb both the boundary conditions and the data, then a convex solution is “close” to a suitable paraboloid and the domain is “close” to a ball with respect to the Hausdorff metric

Tinnitus in elderly patients and prognosis of mild-to-moderate congestive heart failure: a cross-sectional study with a long-term extension of the clinical follow-up

<p>Abstract</p> <p>Background</p> <p>The complex mechanism responsible for tinnitus, a symptom highly prevalent in elderly patients, could involve an impaired control of the microcirculation of the inner ear, particularly in patients with poor blood pressure control and impaired left ventricular (LV) function.</p> <p>Methods</p> <p>In order to define the relationship between the presence of tinnitus and the severity and clinical prognosis of mild-to-moderate chronic heart failure (CHF) in a large population of elderly patients (N = 958), a cross-sectional study was conducted with a long-term extension of the clinical follow-up. Blood pressure, echocardiographic parameters, brain natriuretic peptide (BNP), hospitalization, and mortality for CHF were measured. Multivariate logistic regression analysis was used to assess the association between the presence of tinnitus and some of the prognostic determinants of heart failure.</p> <p>Results</p> <p>The presence of tinnitus was ascertained in 233 patients (24.3%; mean age 74.9 ± 6 years) and was associated with reduced systolic and diastolic blood pressure (123.1 ± 16/67.8 ± 9 vs 125.9 ± 15/69.7 ± 9; <it>P </it>= .027/<it>P </it>= .006), reduced LV ejection fraction (LVEF%; 43.6 ± 15 vs 47.9 ± 14%, <it>P </it>= .001), and increased BNP plasma levels (413.1 ± 480 vs 286.2 ± 357, <it>P </it>= .013) in comparison to patients without symptoms. The distribution of CHF functional class was shifted toward a greater severity of the disease in patients with tinnitus. Combined one-year mortality and hospitalization for CHF (events/year) was 1.43 ± 0.2 in patients with tinnitus and 0.83 ± 0.1 in patients without tinnitus, with an adjusted hazard ratio (HR) of 0.61 (95% confidence interval (CI): 0.37 to 0.93, <it>P </it><.002).</p> <p>Conclusions</p> <p>Our preliminary data indirectly support the hypothesis that tinnitus is associated with a worse CHF control in elderly patients and can have some important clinical implications for the early identification of patients who deserve a more aggressive management of CHF.</p

Stapedotomy versus stapedectomy: an ancient match considered from another point of view

Purpose: Analysis of the differences in inner ear admittance achieved by a large fenestra in comparison with a small fenestra and its effect on bone conduction in stapes surgery. Materials and methods: Description of an interesting case of bilateral otosclerosis with an atypical and symmetrical behaviour of bone conduction, treated with a stapedotomy on the right ear some years before, and recently submitted to stapedectomy on the left year. Results: Concerning the left side, the first complete audiometry was made 15 days after stapedectomy and confirmed a bone conduction improvement, that subsequently increased until almost to the normality 42 days after surgery. The mean postoperative bone conduction difference was 13 dB considering all frequencies; when considering the frequencies between 500 and 2000 Hz the mean difference raised to 20 dB. Conclusions: The reported case, in which the stapedectomy was not scheduled as the first option, but derived from a particular intraoperative situation thus resulting in an almost obligatory choice, permits some interesting conceptual considerations

Idiopathic acute labyrinthine diseases and M&#233;ni&#232;re&#8217;s disease : The necessit y of a multidisciplinary approach.

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