Non-positivity of Groenewold operators

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.

Knowledge beliefs and attitudes of squash venue operators relating to use of protective eyewear

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.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

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.

Asymptotic bifurcation results for quasilinear elliptic operators

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.

The 1899 Orange Free State football team tour of Europe:'race', imperial loyalty and sporting contest

In September 1899 an association football team from Bloemfontein in the Orange Free State, South Africa, arrived in the United Kingdom. The team comprised 16 black South Africans who played under the auspices of the whites-only Orange Free State Football Association and was the first ever South African football team to tour abroad. In a four-month tour the team played 49 matches against opposition in England, France, Ireland, Scotland and Wales. A small but growing body of work focuses on black sport and football in particular and the 1899 tour is referred to in passing in a few publications, although none have attempted to uncover details of the team or the matches that were played in Europe. This article attempts to do this by drawing on a range of sources in South Africa and the United Kingdom and argues the case for the significance of this team for football history in general and South African sports history in particular.

Un phénix linguistique? Le tour narratif va + infinitif renaîtrait-il, en français contemporain, de ses cendres médiévales?

Les études typologiques (Hagège 1993, Bybee et al.1994, Dahl 2000, Bourdin 2008 notamment) ont montré de façon consistante que les indications spatiales (notamment les verbes de mouvement) tendaient à se grammaticaliser en expressions temporelles. La forme itive (en français aller) dans les langues romanes a fait l’objet de ce processus linguistique , et avec succès, puisque, en tant qu’auxiliaire d’un verbe à l’infinitif ou au participe présent (et moins fréquemment au participe passé), elle est à même d’offrir, au cours de son histoire, pas moins de onze emplois grammaticalisés (Bres et Labeau à paraître). Nous nous intéresserons dans cet article, qui ne portera que sur le français, à l’emploi que nous nommerons, avec Larreya (2005) et Lansari (2009), narratif: il apparaît en textualité narrative, dont les propositions du premier plan sont régies par la relation de progression (Labov 1972/1978). Cet emploi que le français a connu jusqu’au début du XVIIème (1) tend, sur des bases peut-être différentes, à se répandre aujourd’hui (2): (1) Sur ces propos, feirent leur accord, et, en regardant le lieu le plus propre pour faire ceste belle oeuvre, elle vat dire qu'elle n'en sçavoit poinct de meilleure ne plus loing de tout soupson, que une petite maison qui estoit dedans le parc, où il y avoit chambre et lict tout à propos. Le gentil homme, qui n'eust trouvé nul lieu mauvais, se contenta de cestuy-là. (Navarre M. de, L'Heptaméron, 1550) (2) (…) Teddy Pendergrass est remarqué par Harold Melvin, leader du quintette vocal The Blue Notes. Il rejoint alors la formation, qui va enchaîner une succession de tubes. En 1976, Teddy Pendergrass décide de mener une carrière solo et quitte les Blue Notes . Il va régulièrement occuper les premières places des meilleures ventes de disques aux USA. (Le Monde, Obituaire de T. Pendergrass, 27 .1. 2010)

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

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.