Distributional Energy-Momentum Densities of Schwarzschild Space-Time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\tilde T_\mu^{\nu}(x)$ of the gravitational source and the gravitational energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions $\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and $\tilde t_\mu^{\nu}=0$, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like $\delta^{(3)}(x)/r^3$ and [\delta^{(3)}(x)}]^2, as well as other terms, which are singular at $x=0$. It is pointed out that the well-known expression $R^{\rho\sigma\mu\nu}({}) R_{\rho\sigma\mu\nu}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$ is not correct, if we define $1/r^6 = \lim_{\epsilon\to 0}1/(r^2+\epsilon^2)^3$.}Comment: 21 pages, LaTeX, uses amssymb.sty. To appear in Prog. Theor. Phys. 98 (1997

Space-centred information management approach to improve CAD-based healthcare building design

This study focuses on developing a space-centred CAD tool to enable designers to effectively manage and implement the information of design guidance information and user requirements during design processes, especially for the stages of design briefing and conceptual design. It aims to structure and store design guidance and user requirements for healthcare building design into a relational database, and link them to relevant space entities in design plans. The tool is developed on the platform of Autodesk Architecture Desktop (ADT). It also enables users to store and retrieve pictures associated with textual information, because pictures have been always used by designers as an effective medium to represent and deliver design information and knowledge. This can give users directly visual and more understandable perceptions of the design guidance. The tool is fully embedded with Autodesk AutoCAD systems to ensure the application of this tool being fully merged with CAD-based design process. A set of design guidance about Alzheimer clinic built environments are adopted as a sample to demonstrate and validate the tool. Moreover, the scenario of expanding this application to more broad areas has also been foreseen

The Gaussian Multiple Access Diamond Channel

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$-letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.Comment: submitted to IEEE Transactions on Information Theor

Engaging in spaces: How mature distance students fit study into their homes and lives

In order to fit study around family and work, a third of mature aged tertiary students in New Zealand study by distance. By enabling students to study when and where they want, distance study is said to overcome the barriers of space and time. But space and time must still be found and the blurring of the physical boundaries between study and home creates new challenges. While much has been written about how distance students juggle time, little has considered how they manage space; yet it is often the availability of an appropriate learning space that determines not just when and where they study, but the quality of their engagement. This qualitative study, following 19 mature aged distance students and their families through their first semester, examines how the students carved learning spaces from their busy lives, the nature of those spaces, and the impact this had on their engagement. For some, a space without other people was the essential characteristic and they achieved this through either a physical separation strategy such as studying at work, or a temporal separation strategy such as studying only when children were at school. For others, isolation was a barrier to their engagement and they gravitated to shared living spaces. Individual lifeload, context, and personal preference mean there are no right or wrong choices, but family support is a critical influence on the success of different strategies