Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.

Local Impacts of Unconventional Gas Development within Pennsylvania's Marcellus Shale Region: Gauging Boomtown Development through the Perspectives of Educational Administrators

Using survey and interview data gathered from educators and educational administrators, we investigate school and community impacts of unconventional gas extraction within Pennsylvania's Marcellus Shale region. Respondents in areas with high levels of drilling are significantly more likely to perceive the effects of local economic gains, but also report increased inequality, heightened vulnerability of disadvantaged community members, and pronounced strains on local infrastructure. As community stakeholders in positions of local leadership, school leaders in areas experiencing Marcellus Shale natural gas extraction often face multiple decision-making dilemmas. These dilemmas occur in the context of incomplete information and rapid, unpredictable community change involving the emergence of both new opportunities and new insecurities.