The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight

We extend the Jang equation proof of the positive energy theorem due to R. Schoen and S.-T. Yau from dimension $n=3$ to dimensions $3 \leq n <8$. This requires us to address several technical difficulties that are not present when $n=3$. The regularity and decay assumptions for the initial data sets to which our argument applies are weaker than those of R. Schoen and S.-T. Yau. In recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a different proof of the full positive mass theorem in dimensions $3 \leq n < 8$. We pointed out that this theorem can alternatively be derived from our density argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy

Black Holes with Zero Mass

We consider the spacetimes corresponding to static Global Monopoles with interior boundaries corresponding to a Black Hole Horizon and analyze the behavior of the appropriate ADM mass as a function of the horizon radius r_H. We find that for small enough r_H, this mass is negative as in the case of the regular global monopoles, but that for large enough r_H the mass becomes positive encountering an intermediate value for which we have a Black Hole with zero ADM mass.Comment: 10 pages, 2 ps figures, REVTeX, some minor change

Disorder-induced pseudodiffusive transport in graphene nanoribbons.

We study the transition from ballistic to diffusive and localized transport in graphene nanoribbons in the presence of binary disorder, which can be generated by chemical adsorbates or substitutional doping. We show that the interplay between the induced average doping (arising from the nonzero average of the disorder) and impurity scattering modifies the traditional picture of phase-coherent transport. Close to the Dirac point, intrinsic evanescent modes produced by the impurities dominate transport at short lengths giving rise to a regime analogous to pseudodiffusive transport in clean graphene, but without the requirement of heavily doped contacts. This intrinsic pseudodiffusive regime precedes the traditional ballistic, diffusive, and localized regimes. The last two regimes exhibit a strongly modified effective number of propagating modes and a mean free path which becomes anomalously large close to the Dirac point

Designing fractional factorial split-plot experiments with few whole-plot factors

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73673/1/j.1467-9876.2003.05029.x.pd

Family Business CEO Succession: Examining Personal Retirement Expectations

Retirement well-being expectations of incumbent family owned business CEOs is a critical precursor to successful succession events. The significant antecedents to retirement well-being expectation are family relationships, wealth management and transfer, leadership succession and development, and continuity and viability of the firm. Using data from a survey of 256 family firm CEOs we demonstrate those relationships and show a very strong connection between retirement well-being expectation and firm performance. Study results further our premise that antecedents to retirement well-being expectation are indirectly tied to the overall health and performance of the family firm

Positivity of Quasilocal Mass

Motivated by the important work of Brown adn York on quasilocal energy, we propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with positive intrinsic curvature in a spacetime. We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface.Comment: 4 pages; final published versio

Statistically designed experiments to screen chemical mixtures for possible interactions.

For the accurate analysis of possible interactive effects of chemicals in a defined mixture, statistical designs are necessary to develop clear and manageable experiments. For instance, factorial designs have been successfully used to detect two-factor interactions. Particularly useful for this purpose are fractionated factorial designs, requiring only a fraction of all possible combinations of a full factorial design. Once the potential interaction has been detected with a fractionated design, a more accurate analysis can be performed for the particular binary mixtures to ensure and characterize these interactions. In this paper this approach is illustrated using an in vitro cytotoxicity assay to detect the presence of mixtures of Fusarium mycotoxins in contaminated food samples. We have investigated interactions between five mycotoxin species (Trichothecenes, Fumonisins, and Zearalenone) using the DNA synthesis inhibition assay in L929 fibroblasts. First, a central composite design was applied to identify possible interactive effects between mycotoxins in the mixtures (27 combinations from 5(5) possible combinations). Then two-factor interactions of particular interest were further analyzed by the use of a full factorial design (5 x 5 design) to characterize the nature of those interactions more precisely. Results show that combined exposure to several classes of mycotoxins generally results in effect addition with a few minor exceptions indicating synergistic interactions. In general, the nature of the interactions characterized in the full factorial design was similar to the nature of those observed in the central composite design. However, the magnitude of interaction was relatively small in the full factorial design

Negative Energy Density in Calabi-Yau Compactifications

We show that a large class of supersymmetric compactifications, including all simply connected Calabi-Yau and G_2 manifolds, have classical configurations with negative energy density as seen from four dimensions. In fact, the energy density can be arbitrarily negative -- it is unbounded from below. Nevertheless, positive energy theorems show that the total ADM energy remains positive. Physical consequences of the negative energy density include new thermal instabilities, and possible violations of cosmic censorship.Comment: 25 pages, v2: few clarifying comments and reference adde

Fate of Kaluza-Klein Bubble

We numerically study classical time evolutions of Kaluza-Klein bubble space-time which has negative energy after a decay of vacuum. As the zero energy Witten's bubble space-time, where the bubble expands infinitely, the subsequent evolutions of Brill and Horowitz's momentarily static initial data show that the bubble will expand in terms of the area. At first glance, this result may support Corley and Jacobson's conjecture that the bubble will expand forever as well as the Witten's bubble. The irregular signatures, however, can be seen in the behavior of the lapse function in the maximal slicing gauge and the divergence of the Kretchman invariant. Since there is no appearance of the apparent horizon, we suspect an appearance of a naked singularity as the final fate of this space-time.Comment: 13 pages including 10 figures, RevTeX, epsf.sty. CGPG-99/12-8, RESCEU-6/00 and DAMTP-2000-30. To appear in Phys. Rev.

Some Curvature Problems in Semi-Riemannian Geometry

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of Lorentzian metrics which satisfy the dominant energy condition.Comment: 25 pages, LaTeX, 4 figure