Compactness of the space of causal curves

We prove that the space of causal curves between compact subsets of a separable globally hyperbolic poset is itself compact in the Vietoris topology. Although this result implies the usual result in general relativity, its proof does not require the use of geometry or differentiable structure.Comment: 15 page

Comment on "Effect of growth interruptions on the light emission and indium clustering of InGaN/GaN multiple quantum wells" [Appl. Phys. Lett. 79, 2594 (2001)]

This entry is a comment on "Effect of growth interruptions on the light emission and indium clustering

Generalization of the Calogero-Cohn Bound on the Number of Bound States

It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential $V(r)$, in each angular momentum state, that is, bounds containing only the integral $\int^\infty_0 |V(r)|^{1/2}dr$, the condition $V'(r) \geq 0$ is not necessary, and can be replaced by the less stringent condition $(d/dr)[r^{1-2p}(-V)^{1-p}] \leq 0, 1/2 \leq p < 1$, which allows oscillations in the potential. The constants in the bounds are accordingly modified, depend on $p$ and $\ell$, and tend to the standard value for $p = 1/2$.Comment: 1 page. Correctly formatted version (replaces previous version

Exploitation of ERTS-1 imagery utilizing snow enhancement techniques

Photogeological analysis of ERTS-simulation and ERTS-1 imagery of snowcovered terrain within the ERAP Feather River site and within the New England (ERTS) test area provided new fracture detail which does not appear on available geological maps. Comparative analysis of snowfree ERTS-1 images has demonstrated that MSS Bands 5 and 7 supply the greatest amount of geological fracture detail. Interpretation of the first snow-covered ERTS-1 images in correlation with ground snow depth data indicates that a heavy blanket of snow (more than 9 inches) accentuates major structural features while a light "dusting", (less than 1 inch) accentuates more subtle topographic expressions. An effective mail-based method for acquiring timely ground-truth (snowdepth) information was established and provides a ready correlation of fracture detail with snow depth so as to establish the working limits of the technique. The method is both efficient and inexpensive compared with the cost of similarly scaled direct field observations

Caddo Ceramics on the Red River in North Central Texas

Caddo ceramics manufactured after A.D. 900 were widely traded in Texas, being found in some quantity on North Central, East Central, Central, and inland Southeast Texas archeological sites. They were also traded with prehistoric peoples in the Midwest (as far north as Iowa and Illinois) and the Southeastern U.S. While archeologists have known this for some time, much of the ceramic evidence for prehistoric Caddoan trade and exchange with other Native Americans has not been systematically compiled and studied, as became apparent during a recent review of the prehistoric and historic aboriginal pottery in Texas. Consequently, Caddoan archeologists are not yet in the position to confidently discuss the scope, timing, or direction of trade/exchange between Caddoan groups and surrounding non-Caddoan communities, or explore changes in the nature of social and economic relationships between particular Caddo groups and other prehistoric peoples. This paper represents part of our initial efforts to begin systematically compiling archeological information on the distribution and character of Caddo ceramic sherds and vessels outside what is considered the southern Caddoan archaeological area. In it, we report on Early and Late Caddo ceramics found by Dr. Ernest R. Martin at two sites along the Red River in North Central Texas, some 130 km or more west of the westernmost Caddo settlements on the Red River in Northeast Texas

Spin relaxation in diluted magnetic semiconductor quantum dots

Electron spin relaxation induced by phonon-mediated s-d exchange interaction in a II-VI diluted magnetic semiconductor quantum dot is investigated theoretically. The electron-acoustic phonon interaction due to piezoelectric coupling and deformation potential is included. The resulting spin lifetime is typically on the order of microseconds. The effectiveness of the phonon-mediated spin-flip mechanism increases with increasing Mn concentration, electron spin splitting, vertical confining strength and lateral diameter, while it shows non-monotonic dependence on the magnetic field and temperature. An interesting finding is that the spin relaxation in a small quantum dot is suppressed for strong magnetic field and low Mn concentration at low temperature.Comment: 11 pages, 11 figures, to be published in Phys. Rev.

Leaky vessels as a potential source of stromal acidification in tumours

Malignant tumours are characterised by higher rates of acid production and a lower extracellular pH than normal tissues. Previous mathematical modelling has indicated that the tumour-derived production of acid leads to a gradient of low pH in the interior of the tumour extending to a normal pH in the peritumoural tissue. This paper uses mathematical modelling to examine the potential of leaky vessels as an additional source of stromal acidification in tumours. We explore whether and to what extent increasing vascular permeability in vessels can lead to the breakdown of the acid gradient from the core of the tumour to the normal tissue, and a progressive acidification of the peritumoural stroma. We compare our mathematical simulations to experimental results found in vivo with a tumour implanted in the mammary fat pad of a mouse in a window chamber construct. We find that leaky vasculature can cause a net acidification of the normal tissue away from the tumour boundary, though not a progressive acidification over time as seen in the experiments. Only through progressively increasing the leakiness can the model qualitatively reproduce the experimental results. Furthermore, the extent of the acidification predicted by the mathematical model is less than as seen in the window chamber, indicating that although vessel leakiness might be acting as a source of acid, it is not the only factor contributing to this phenomenon. Nevertheless, tumour destruction of vasculature could result in enhanced stromal acidification and invasion, hence current therapies aimed at buffering tumour pH should also examine the possibility of preventing vessel disruption