894 resultados para Averaging operators


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Mode of access: Internet.

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A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Lionville densities, leading to what may be termed Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Lionville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.

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Sports venues are in a position to potentially influence the safety practices of their patrons. This study examined the knowledge, beliefs and attitudes of venue operators that could influence the use of protective eyewear by squash players. A 50% random sample of all private and public squash venues affiliated with the Victorian Squash Federation in metropolitan Melbourne was selected. Face-to-face interviews were conducted with 15 squash venue operators during August 2001. Interviews were transcribed and content and thematic analyses were performed. The content of the interviews covered five topics: (1) overall injury risk perception, (2) eye injury occurrence, (3) knowledge, behaviors, attitudes and beliefs associated with protective eyewear, (4) compulsory protective eyewear and (5) availability of protective eyewear at venues. Venue operators were mainly concerned with the severe nature of eye injuries, rather than the relatively low incidence of these injuries. Some venue operators believed that players should wear any eyewear, rather than none at all, and believed that more players should use protective eyewear. Generally, they did not believe that players with higher levels of experience and expertise needed to wear protective eyewear when playing. Only six venues had at least one type of eyewear available for players to hire or borrow or to purchase. Operators expressed a desire to be informed about correct protective eyewear. Appropriate protective eyewear is not readily available at squash venues. Better-informed venue operators may be more likely to provide suitable protective eyewear.

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In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

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We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

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Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.