This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for margina...

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for margina...

This research combined three distinctly unique and separate measures of corruption into one corruption factor, so as to yield a robust measurement approach to further understand the political and socioeconomic variables of corruption. The findings show that a strong significant variable in measuring corruption is the personal marginal-tax rate, especially in hierarchical based nations. The high...

Qingyu Feng. M.S.A.B.E., Purdue University, December 2013. Biomass Production and Hydrological/Water Quality Impacts of Perennial Crop Production on Marginal Land. Major Professor: Indrajeet Chaubey. Marginal land has been proposed to be a viable choice for biomass production to meet the biofuel development goal set by Energy Independence and Security Act (EISA). However, very little informatio...

Lakes in direct contact with glaciers (ice-marginal lakes) are found across alpine and polar landscapes. Many studies characterize ice-marginal lake behavior over multi-decadal timescales using either episodic ~annual images or multi-year mosaics. However, lakes dynamic features that experience short-term (i.e., day to year) variations area volume superimposed on longer-term trends. Through ali...

Bio-energy from energy plants is expected to play an increasing role in the future energy system, with benefits in terms of reducing greenhouse gas emissions and improving energy security. Pistacia chinensis is believed to be one of the most promising non-food input for biodiesel production. This study focused on the marginal land availability for developing Pistacia chinensis-based bioenergy i...