Bounds for the number of nodes in Chebyshev type quadrature formulas

AbstractWe consider Chebyshev type quadrature formulas on an interval, i.e., quadrature formulas where all nodes are weighted equally. Using a topological method, we give an upper bound for the minimum number of nodes needed in order to achieve a certain degree of precision. We also consider the corresponding problem on the d-dimensional sphere Sd

L’auteur réincarné ou de l’interprétation comme folie. À propos de La Guérison de Roberto Gac

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BINAURAL LOUDNESS OF MOVING SOURCES IN FREE FIELD: PERCEPTUAL MEASUREMENTS VERSUS AT-EAR LEVELS

International audienceMost investigations on the variations of loudness with the spatial position of a sound source have been made for static sounds. The purpose of this work was to study the loudness of a moving source. By analogy with studies on difference in loudness between sounds increasing or decreasing in intensity (without movement of the source), we studied the global loudness of a moving sound. The analogy with the sounds whose intensity varies is direct because the at-ear level depends on the position of the source, so a moving sound will create levels that vary over time at the entrance of the auditory canal. We measured the overall loudness of a moving source as a function of the starting and ending positions of the stimulus and of its direction of rotation. Overall, we did not find any overall loudness difference according to the direction of variation of the source. Moreover, the results obtained with a static sound seem to confirm, with absolute magnitude estimation, the amount of directional loudness sensitivity measured previously with an adaptive method. In free field, loudness depends on the position of the sound source (Sivonen and Ellermeier, 2006). In order to quantify the effect of the incidence angle on loudness, the directional loudness sensitivity (DLS) is measured. DSL is defined as the level difference required for equal loudness between a frontal reference sound (azimuth 0°, elevation 0°) and a test sound at a given position. A negative DLS means that the test sound has been perceived softer than the frontal sound and vice versa. In a previous study, we showed a decrease in DLS with an increase in azimuth of an amount of more than 10 dB on average (25 listeners, Meunier et al., 2016). Different studies have also examined the loudness of sounds that increase and sounds that decrease in level. For sounds that only differ in temporal envelop, it has been shown that the global loudness of a sound whose level increases is greater than the global loudness of a sound whose level decreases (Ponsot et al., 2015a, 2015b). This phenomenon has been called asymmetry in loudness. When a sound source is moving around a listener, the at-ear level of the sound varies. Moreover, if we refer to the studies on directional loudness, its loudness should also vary. The aim of the work presented here was to explore how global loudness of moving sounds is formed and the main point was to determine whether there is an asymmetry between sounds that move in opposite directions as their level and loudness also vary in opposite directions

Massively Parallel Spectral Element Large Eddy Simulation of a Turbulent Channel Using Wall Models

Wall-bounded turbulent flows are prevalent in engineering and industrial applications. Walls greatly affect turbulent characteristics in many ways including production and propagation of turbulent stresses. While computational fluid dynamics can be used as an important design tool, its use is hindered due to the fine-mesh requirements in the near-wall region to capture all of the pertinent turbulent data. To resolve all relevant scales of motion, the number of grid points scales with Reynolds number as N ≈ Re9/4, making it nearly impossible to solve real engineering problems, most of which feature high Reynolds numbers. A method to help alleviate the resolution requirements is the use of wall models. This method allows for a coarser mesh to be used in which the near-wall region is modeled and the first grid point is placed in the log-law region. The shear stress at the wall is correlated with the velocity at a point outside the near-wall region, drastically reducing the number of elements required and reducing the computational time and cost of the simulation. The goal of this study was to test the speed increase and element reduction capabilities of combining a wall function solution with the massively-parallel, spectral element solver, Nek5000, and verify the method using a turbulent channel simulation. The first grid point is placed at y+ = 100, in the log-law region, for Reτ = 950 and the sub-grid scales are modeled using a dynamic Smagorinski model. The results are then compared to a DNS performed by Jimenez and Hoyas for model verification

De Naoorlogse Oostendse Revues

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Comparison of the Long-Term Effect of Positioning the Cathode in tDCS in Tinnitus Patients

Objective: Transcranial direct current stimulation (tDCS) is one of the methods described in the literature to decrease the perceived loudness and distress caused by tinnitus. However, the main effect is not clear and the number of responders to the treatment is variable. The objective of the present study was to investigate the effect of the placement of the cathode on the outcome measurements. Methods: Patients considered for the trial were chronic non-pulsatile tinnitus patients with complaints for more than 3 months and a Tinnitus Functional Index (TFI) score that exceeded 25. The anode was placed on the right dorsolateral prefrontal cortex (DLPFC). In the first group—“bifrontal”—the cathode was placed on the left DLPFC, while in the second group—“shoulder”—the cathode was placed on the shoulder. Each patient received two sessions of tDCS weekly and eight sessions in total. Evaluations took place on the first visit for an ENT consultation, at the start of therapy, after eight sessions of tDCS and at the follow-up visit, which took place 84 days after the start of the therapy. Subjective outcome measures such as TFI, Visual Analog Scales (VAS) for loudness and percentage of consciousness of tinnitus were administered in every patient. Results: There was no difference in the results for tinnitus loudness and the distress experienced between the placement of the cathode on the left DLPFC or on the shoulder. In addition, no statistically significant overall effect was found between the four test points. However, up to 39.1% of the patients experienced a decrease in loudness, measured by the VAS for loudness. Moreover, 72% of those in the bifrontal group, but only 46.2% of those in the shoulder group reported some improvement in distress. Conclusion: While some improvement was noted, this was not statistically significant. Both electrode placements stimulated the right side of the hippocampus, which could be responsible for the effect found in both groups. Further research should rule out the placebo effect and investigate alternative electrode positions