Complete curvature homogeneous pseudo-Riemannian manifolds

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.Comment: Update paper to fix misprints in original versio

Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull back has finite Fourier series on

Shelter as Sanctuary: A Narrative Inquiry of the Experience of Homelessness

What is the meaning of homelessness and how does it translate into a better understanding of what the experience of homelessness represents? Exploring the experiences of those who are homeless and the meaning of those experiences is essential when attempting to gain insight and improve service response to those who are homeless. Narrative inquiry is used in this dissertation to tell a story of homelessness from social and personal perspectives. Ultimately, my own understanding of the social and personal dictate the story of homelessness presented in this narrative. It provides an opportunity to better understand what it means to be homeless, why individuals seek shelter, and what can happen when individuals living a homeless experience are called upon to experience their lives in their own words. What is revealed through the personal stories suggest a need for sanctuary. Sanctuary in this narrative represents respite, security, a place to decide next steps, and ultimately, for a few, a place for transition. An emergency shelter program for the homeless comes to represent sanctuary for the twenty participants in this study. It is during this experience of sanctuary that participants come to "confirm, resist, and eventually maintain or transform the accepted norm" (Richardson, 2001, p. 37) of what it means to live in a homeless circumstance. The internalized cultural self (Swandt, 1999) emerges as the dominant influence in telling the story of homelessness, both on the part of study participants and that of the author. Sanctuary emerges as a key theme from the personal stories, but the act of self-reflection when telling one's story becomes the catalyst for a new thinking about how participants view their homeless circumstance and their life experiences. That self-reflection proves to be an unexpected invitation to the reconstruction of one's personal story of homelessness, and an invitation for me to consider a different kind of service response. It is in this narrative, the beginning of an alternative model for emergency shelter services, where opportunties for sanctuary or respite are discussed as key needs for participants of this study. In addition, a proposed sanctuary model of service intervention is presented, where traditional emergency services are available, but with a caveat of service support that elicits the personal stories of those who are willing to reconstruct their life experiences and begin the process of narrating a different experience that holds transitional implications for their current homeless circumstance

Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for $2\le k\le s$; they are k-timelike higher order Jordan Osserman for $s+2\le k\le 2s$, and they are not k timelike higher order Jordan Osserman for $2\le s\le s+1$.Comment: Update bibliography, fix minor misprint

Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction

The next-to-leading term of the renormalized stress-energy tensor of the quantized massive field with an arbitrary curvature coupling in the spacetime of the Schwarzschild black hole is constructed. It is achieved by functional differentiation of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $a_{3}$ and $a_{4}.$ The back reaction of the quantized field upon the Schwarzschild black hole is briefly discussed

The Heat Kernel Coefficients to the Matrix Schr\"odinger Operator

The heat kernel coefficients $H_k$ to the Schr\"odinger operator with a matrix potential are investigated. We present algorithms and explicit expressions for the Taylor coefficients of the $H_k$. Special terms are discussed, and for the one-dimensional case some improved algorithms are derived.Comment: 16 pages, Plain TeX, 33 KB, no figure

Evaluation of the Oxygen Concentrator Prototypes: Pressure Swing Adsorption Prototype and Electrochemical Prototype

An oxygen concentrator is needed to provide enriched oxygen in support of medical contingency operations for future exploration human spaceflight programs. It would provide continuous oxygen to an ill or injured crew member in a closed cabin environment. Oxygen concentration technology is being pursued to concentrate oxygen from the ambient environment so oxygen as a consumable resource can be reduced. Because oxygen is a critical resource in manned spaceflight, using an oxygen concentrator to pull oxygen out of the ambient environment instead of using compressed oxygen can provide better optimization of resources. The overall goal of this project is to develop an oxygen concentrator module that minimizes the hardware mass, volume, and power footprint while still performing at the required clinical capabilities. Should a medical event occur that requires patient oxygenation, the release of 100 percent oxygen into a small closed cabin environment can rapidly raise oxygen levels to the vehicles fire limit. The use of an oxygen concentrator to enrich oxygen from the ambient air and concentrate it to the point where it can be used for medical purposes means no oxygen is needed from the ultra-high purity (99.5+% O2) oxygen reserve tanks. By not adding oxygen from compressed tanks to the cabin environment, oxygen levels can be kept below the vehicle fire limit thereby extending the duration of care provided to an oxygenated patient without environmental control system intervention to keep the cabin oxygen levels below the fire limits. The oxygen concentrator will be a Food and Drug Administration (FDA) clearable device. A demonstration unit for the International Space Station (ISS) is planned to verify the technology and provide oxygen capability. For the ISS, the demonstration unit should not exceed 10 kg (approximately 22 lb), which is the soft stowage mass limit for launch on resupply vehicles for the ISS. The unit's size should allow for transport within the spacecraft to an ill crewmember. The user interface needs to be designed for ease of use by the local care provider and with consideration to the limited amount of training available to the astronaut corps for medical equipment and procedures

Spatial curvature effects on molecular transport by diffusion

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the known solution of Fick's law of diffusion in the flat space limit. In the biological context, this result would be useful in understanding the variations in the diffusion rates of integral proteins and other molecules on membranes.Comment: 10 page

Non-commutative geometry and the standard model vacuum

The space of Dirac operators for the Connes-Chamseddine spectral action for the standard model of particle physics coupled to gravity is studied. The model is extended by including right-handed neutrino states, and the S0-reality axiom is not assumed. The possibility of allowing more general fluctuations than the inner fluctuations of the vacuum is proposed. The maximal case of all possible fluctuations is studied by considering the equations of motion for the vacuum. Whilst there are interesting non-trivial vacua with Majorana-like mass terms for the leptons, the conclusion is that the equations are too restrictive to allow solutions with the standard model mass matrix.Comment: 21 pages. v2: some comments improve

Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities

Eigenmodes of electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE modes and one polarization for TM modes, giving rise to a total of (D-1) polarizations. In case of a D-dimensional ball, the eigenfrequencies of electromagnetic field with perfectly conducting boundary condition coincides with the eigenfrequencies of gauge one-forms with relative boundary condition; whereas the eigenfrequencies of electromagnetic field with infinitely permeable boundary condition coincides with the eigenfrequencies of gauge one-forms with absolute boundary condition. Casimir energy for a D-dimensional spherical shell configuration is computed using both cut-off regularization and zeta regularization. For a double spherical shell configuration, it is shown that the Casimir energy can be written as a sum of the single spherical shell contributions and an interacting term, and the latter is free of divergence. The interacting term always gives rise to an attractive force between the two spherical shells. Its leading term is the Casimir force acting between two parallel plates of the same area, as expected by proximity force approximation.Comment: 28 page