A class of Schrodinger operators with decaying oscillatory potentials

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.Comment: 18 page

Associations between neighbourhood street pattern, neighbourhood socioeconomic status and sleep in adults

Sleep duration is a risk factor for poor health and all-cause mortality. Evidence suggests that neighbourhood characteristics such as built environment and socioeconomic status (SES) may affect sleep duration in adults. This study examined the relationship between neighbourhood built environment (i.e., measured via the street pattern) and SES with sleep duration in adults (n = 797) from 12 neighbourhoods in Calgary (Canada). Covariate adjusted linear and multinomial logistic regression models estimated the associations between street pattern (grid, warped-grid, curvilinear), SES and sleep duration. We also tested if the interaction between street pattern and SES was associated with sleep duration. Although neighbourhood street pattern and neighbourhood SES were not independently associated with sleep, the interaction between street pattern and neighbourhood SES, was associated with mean sleep duration. Individuals living in curvilinear low SES neighbourhoods had the shortest sleep duration (6.93 h per day; 95% CI 6.68, 7.18), while those living in curvilinear high SES neighbourhoods slept the longest (7.43 h per day; 95% CI 7.29, 7.57). Neighbourhood street pattern and SES, as well as their interaction, were not associated with the odds of sleeping shorter or longer than 7 to 8 h per day. Our findings suggest that the combined effect of the neighbourhood built environment and SES is potentially important for influencing sleep duration. More research is needed to understand the complex interrelationships between the built environment, SES, and sleep

Surgical management of pelvic relaxation: retrospective evaluation of 723 cases.

International Urogynecological Journal,Vol 1, N 1, 310,October 1988