Generalizing the Heisenberg uncertainty relation

The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions on the state to which the relation is applied, increasing its generality. The restrictions necessary for the standard inequality to apply are not widely known, and they are discussed in detail. The classical analog of the Heisenberg relation is also derived, and the two are compared. Finally, the modified relation is used to address the apparent paradox that eigenfunctions of the z component of angular momentum L_z do not satisfy the \phi-L_z Heisenberg relation; the resolution is that the restrictions mentioned above make the usual inequality inapplicable to these states. The modified relation does apply, however, and it is shown to be consistent with explicit calculations.Comment: 12 pages, no figures. Contains corrections to errors in the published editio

Human Trafficking: It’s Not Just a Crime

Human trafficking, although commonly conceived of as a crime, is also a matter for the fields of health and public health. Trafficked individuals suffering physical, sexual, and/or psychological abuse can experience acute and chronic health sequelae, bringing them to the attention of health and/or mental health professionals. Communicable infections affect many trafficked individuals and can be transmitted to those not trafficked. The factors that contribute to people being trafficked, like poverty, educational disparities, and systematic oppression based upon identities, are multifaceted and interlinked with other trauma experiences. Incorporation of public health principles into anti-trafficking efforts facilitates a comprehensive and holistic prevention/intervention anti-trafficking strategy. This commentary illustrates how both the health care and public health sectors can contribute to improving the health and well-being of trafficked people, the general public, and to anti-trafficking efforts

Product Differentiation and Film Programming Choice: Do First-Run Movie Theatres Show the Same Films?

We present an empirical analysis of product differentiation using a new dynamic panel data set on film programming choice in a major U.S. metropolitan motion-pictures exhibition market. Using these data, we compute two measures of film programming choice, which allow us to investigate the determinants of strategic product differentiation in a multi-characteristics space. Our evidence is consistent with the idea that the degree of product differentiation between theatre pairs reflects a balance between strategic concerns and contractual constraints. Similarity in one dimension is offset by differentiation in others. Our results further suggest that the degree of product differentiation is negatively related to market size. Finally, we find thta ownership matters theatres under common ownership make more similar programming choices than theatres with different owners.

Souvenir of Mount Desert

Illustrations published as a souvenir of Mount Desert Island, Maine, by Chisolm Bros. of Portland Maine, Sale Agents for Chas. Frey\u27s Original Souvenir Albums, circa 1900