Specific Solvents for Lower Rank Bituminous Coals

The first liquefaction of high-rank bituminous coals by preceding hydrogenation with homogeneous borane or iodine catalysts.

Mapping and Prediction of Coal Workers’ Pneumoconiosis with Bioavailable Iron Content in the Bituminous Coals

Based on the first National Study of Coal Workers' Pneumoconiosis (CWP) and the U.S. Geological Survey database of coal quality, we show that the prevalence of CWP in seven coal mine regions correlates with levels of bioavailable iron (BAI) in the coals from that particular region (correlation coefficient r = 0.94, p < 0.0015). CWP prevalence is also correlated with contents of pyritic sulfur (...

Structured Lower Rank Approximation

A Lower Bound for Succinct Rank Queries

The rank problem in succinct data structures asks to preprocess an array A[1 . . n] of bits into a data structure using as close to n bits as possible, and answer queries of the form Rank(k) = ∑k i=1 A[i]. The problem has been intensely studied, and features as a subroutine in a majority of succinct data structures. We show that in the cell probe model with w-bit cells, if rank takes t time, th...

Equations for Lower Bounds on Border Rank

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...