The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

Ethnography in Congregations

Ethnography is increasingly used in research conducted in congregations. Ethnography can provide rich description and is able to navigate between the stories of congregational members and the story observed by the researcher. Quality ethnography in congregations requires attention to ethics, navigating insider/outsider dynamics, and research aims

Emissions of Hexavalent Chromium From Hard Chromium Plating Operations

This research addresses emissions of hexavalent chromium mist from hard chromium electroplating operations. Most of these emissions are typically captured by a ventilation stack and directed to a pollution control device; those which escape capture are called fugitive emissions. Releases of toxic materials such as hexavalent chromium must be reported annually to the Environmental Protection Agency (EPA) under provisions of the Superfund Amendments and Reauthorization Act (SARA) Title III of 1986 via the Toxic Release Inventory (TRI), Form R. The objectives were: (1) to provide estimates of fugitive hexavalent chromium emissions for the completion of Form R; and (2) to develop a predictive model for stack and fugitive emissions versus process and ventilation parameters. The database for stack emissions included published results from EPA studies. Fugitive release data were generated by field characterization at two operating facilities. Supplemental data for stack releases were also obtained during this field activity. The fugitive releases were documented to represent a small portion of the total atmospheric discharge; in most instances, the fugitive releases were less than the detection capability of the sampling/analytical protocols. Stack releases were successfully correlated with a measure of production activity (ampere-hours), production capacity (mass of chromium in the process bath), tank dimensions (plating bath surface area), and ventilation efficiency (ventilation slot area). This effort was supported by the EPA in the form of a cooperative agreement with the American Electroplaters and Surface Finishers Society (AESF)

Ethnography in Congregations

Ethnography is increasingly used in research conducted in congregations. Ethnography can provide rich description and is able to navigate between the stories of congregational members and the story observed by the researcher. Quality ethnography in congregations requires attention to ethics, navigating insider/outsider dynamics, and research aims

Educating Student Midwives around Dignity and Respect

Focus: There is currently limited information available on how midwifery students learn to provide care that promotes dignity and respect. Background In recent years the importance of dignity in healthcare and treating people with respect has received considerable emphasis in both a national and international context. Aim The aim of this discussion paper is to describe an educational workshop that enables learning to promote dignity and respect in maternity care. Discussion: An interactive workshop, using different creative methods as triggers for learning will be described. Provision of learning opportunities for students around dignity and respect is important to ensure appropriate care is provided in practice. The use of creative methods to inspire has contributed to deep learning within participants. An evaluation of the workshop illustrated how learning impacted on participants practice. Data to support this is presented in this paper Conclusion The use of creative teaching approaches in a workshop setting appears to provide an effective learning opportunity around dignified and respectful care. These workshops have evoked a deep emotional response for some participants, and facilitators must be prepared for this outcome to ensure a safe space for learning

Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type

We consider the Segal-Bargmann transform for a noncompact symmetric space of the complex type. We establish isometry and surjectivity theorems for the transform, in a form as parallel as possible to the results in the compact case. The isometry theorem involves integration over a tube of radius R in the complexification, followed by analytic continuation with respect to R. A cancellation of singularities allows the relevant integral to have a nonsingular extension to large R, even though the function being integrated has singularities.Comment: Final version. To appear in Journal of Functional Analysis. Minor revision