A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from an integral formulation of the radiation condition at infinity. In this Letter, we implement a Fourier-Chebyschev collocation method and show that this approach reduce the computational cost significantly. As a consequence, we give numerical evidence of some convergence estimates available in literature and we study the robustness of the algorithm at low and mid-high frequencies

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented

On deformation of Poisson manifolds of hydrodynamic type

We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.Comment: LaTeX file, 24 page

Investigation of Tinnitus Patients in Italy: Clinical and Audiological Characteristics

Objective. 312 tinnitus sufferers were studied in order to analyze: the clinical characteristics of tinnitus; the presence of tinnitus-age correlation and tinnitus-hearing loss correlation; the impact of tinnitus on subjects' life and where possible the etiological/predisposing factors of tinnitus. Results. There is a slight predominance of males. The highest percentage of tinnitus results in the decades 61–70. Of the tinnitus sufferers, 197 (63.14%) have a hearing deficit (light hearing loss in 37.18% of cases). The hearing impairment results of sensorineural type in 74.62% and limited to the high frequencies in 58.50%. The tinnitus is referred as unilateral in 59.93%, a pure tone in 66.99% and 10 dB above the hearing threshold in 37.7%. It is limited to high frequencies in 72.10% of the patients with sensorineural hearing loss (SNHL) while the 88.37% of the patients with high-frequency SNHL have a high-pitched tinnitus (χ2 = 66.26;P < .005). Conclusion. Hearing status and age represent the principal tinnitus related factors; there is a statistically significant association between high-pitched tinnitus and high-frequency SNHL. There is no significant correlation between tinnitus severity and tinnitus loudness confirming the possibility that neural connection involved in evoking tinnitus-related negative reactions are governed by conditioned reflexes

Physical exercise and Sport activities in patients with and without coronary heart disease

Background: The quantity and intensity of physical activity required for the primary prevention of coronary heart disease remain unclear. Therefore, we examined the association between physical activity and coronary risk. Methods: We studied 100 patients with chest pain, 78 men and 22 women, not older than 65 years, admitted to a coronary care unit. Patients were subdivided in 3 groups: the first group included patients with acute myocardial infarction, the second group included patients with chronic heart disease, the third included patients with non-ischemic chest-pain. A questionnaire on daily physical activity was filled by each patient. Results: A significantly higher percentage of patients with myocardial infarction and coronary heart disease had a sedentary life style compared to patients of the third group. Compared with subjects without heart disease, a significantly higher percentage of patients of the first and second group covered a daily average distance shorter than 500 meters, while a significantly inferior percentage covered a distance longer than 1 Km every day. A significantly lower percentage of patients with coronary heart disease practised sport compared with the third group. At the time of hospitalization a very small percentage of coronary heart disease patients still practised sport. Conclusions: The association between physical activity and reduced coronary risk is clear; in order to obtain benefits it is sufficient just walking every day. Regarding physical activity, continuity is important: patients, who practised sport only in juvenile age, breaking off when older, may lose the obtained advantages