Uncovering Ramanujan's "Lost" Notebook: An Oral History

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's notes, and recent breakthroughs by Ono and others carrying certain important aspects of the Indian mathematician's work into the future. Also presented are historical details related to Ramanujan and his mathematics, perspectives on the impact of his work in contemporary mathematics, and a number of interesting personal anecdotes from Andrews, Berndt and Ono

Coal Resources of the Springfield Coal Bed in Western Kentucky

Historically, the Springfield (Western Kentucky No. 9) coal bed has been the leading source of production in the Western Kentucky Coal Field. The Springfield coal is known for its lateral continuity in terms of both thickness and coal quality. It is estimated to have the largest original and remaining resource in the Western Kentucky Coal Field (Greb and others, 1992)

Coal Availability in Western Kentucky

Fourteen quadrangles in five separate areas of the Western Kentucky Coal Field were studied to determine what factors affect the availability of coal for mining. Each study area consisted of at least two adjacent 7.5-minute quadrangles in order to account for the geologic variability across broad distances in western Kentucky, and determine how this variability affects availability. Areas both north and south of the Rough Creek Fault System were selected to measure the effect of different geologic, structural, and overburden settings on coal availability. The study emphasized the coals occurring stratigraphically between the Springfield and the Baker. About 90 percent of western Kentucky coal resources is associated with only six beds, and one bed, the Springfield (W. Ky. No. 9), constitutes 25 percent of the entire estimate. Seventy percent of the resource is greater than 56 in. thick. Most mining in the Western Kentucky Coal Field is currently by underground methods; only 25 percent is by surface mining. A geographic information system (GIS) was used to estimate tonnages. Point data were obtained from over 5,000 drill-hole and geophysical-log descriptions, and included coal thickness, parting thickness, elevation, and stratigraphic position. Outcrops were digitized from U.S. Geological Survey (USGS) 7.5-minute geologic quadrangle maps, and land-use restrictions from USGS 7.5-minute topographic quadrangle maps. Mined-out areas were obtained from the Kentucky Department of Mines and Minerals, and locations of oil and gas wells from the Kentucky Geological Survey. A digital elevation model was obtained from the U.S. Geological Survey. Land-use restrictions can apply to both surface and deep mining. Technological restrictions in this study generally apply only to deep mining, and include barriers around existing mines, mining within 40 vertical feet of a seam, active oil and gas wells, coal too thin for current underground mining methods (less than 28 in.), and small mine blocks. Many technological restrictions in western Kentucky could be overcome if the relatively low profit margins in the region increased. Tonnage estimates for each bed are reported by categories of coal thickness, overburden thickness, and reliability of the estimate. Thickness categories used in this study are 14 to 28 in., 28 to 42 in., and greater than 42. in. Overburden categories are surface-mineable, deep-mineable, and too deep to mine with current technology. Reliability categories, based on distance from coal-thickness measurements, are measured (within % mi of a data point), indicated (between % and % mi), inferred (between % and 3 mi), and hypothetical (beyond 3 mi). Total original resources for the assessed coals in the 14 studied quadrangles are estimated at 5.55 billion tons (BT). Almost half this total is accounted for by the Springfield coal, and nearly a quarter by the Baker. About 77 percent of the coal is considered deep-mineable. A total of 1.084 BT, or 20 percent of he original resource, has been mined out or lost to mining. Thus, 4 BT, or 80 percent of original resources, remain. The average amount of restricted coal is 26 percent of original resources, and 88 percent of this restricted amount is by technological factors. The most important technological restriction was coal too thin to mine. Small interburden thickness between two mineable seams is a key factor in some areas; other locally important factors are mine barriers and small mine blocks. The average availability of coal in the 14 studied quadrangles is 54 percent. The results by quadrangle range from 9 to 91 percent, which confirms the necessity of studying larger areas. Deep-mineable coal between 28 and 42 in. thick and surface-mineable coal between 14 and 28 in. thick is considered available, but uneconomic. The uneconomic resources account for 14 percent of the original resource, leaving 40 percent of the coal that is both available and economic

TAC-1, a Regulator of Microtubule Length in the C. elegans Embryo

AbstractRegulation of microtubule growth is critical for many cellular processes, including meiosis, mitosis, and nuclear migration. We carried out a genome-wide RNAi screen in Caenorhabditis elegans to identify genes required for pronuclear migration, one of the first events in embryogenesis requiring microtubules. Among these, we identified and characterized tac-1 a new member of the TACC (Transforming Acidic Coiled-Coil) family [1]. tac-1(RNAi) embryos exhibit very short microtubules nucleated from the centrosomes as well as short spindles. TAC-1 is initially enriched at the meiotic spindle poles and is later recruited to the sperm centrosome. TAC-1 localization at the centrosomes is regulated during the cell cycle, with high levels during mitosis and a reduction during interphase, and is dependent on aurora kinase 1 (AIR-1), a protein involved in centrosome maturation [2]. tac-1(RNAi) embryos resemble mutants of zyg-9[3], which encodes a previously characterized centrosomal protein of the XMAP215 family and was also found in our screen. We show that TAC-1 and ZYG-9 are dependent on one another for their localization at the centrosome, and this dependence suggests that they may function together as a complex. We conclude that TAC-1 is a major regulator of microtubule length in the C. elegans embryo

Iron absorption and oxidant stress during erythropoietin therapy in very low birth weight premature infants: a cohort study

BACKGROUND: Iron supplementation may be associated with oxidative stress particularly in premature infants. Our purpose was to examine 1) early supplemental iron during treatment with erythropoietin (EPO) and oxidative stress; 2) enhanced iron absorption during EPO in those infants receiving human milk. Therefore, we determined the effect of erythropoietin plus supplemental iron intakes (4 mg/kg/d) on antioxidant status and iron incorporation. METHODS: Ten very-low-birth-weight infants who were enterally fed and receiving either human milk or formula were followed for 4 weeks during erythropoietin therapy; blood and urine were collected at 3 times; baseline, 2 and 4 weeks later. Once oral feeds commenced the study protocol was initiated. After baseline blood collection, a dose of Fe(57 )was administered. Two weeks later, a dose of Fe(58 )was administered as ferrous chloride to determine the effect of human-milk or formula on iron incorporation into RBCs. RESULTS: Infants started the study at 35 ± 13 days. Incorporation of isotope into RBCs did not differ between formula fed for Fe(57 )(mean incorporation 8 ± 2.9 n = 3) compared to human-milk fed infants (8.7 ± 5 n = 7) nor for Fe(58 )(6 ± 2.7 n = 3 vs. 8.6 ± 5 n = 7). Tissue damage measured by malondialdehyde in plasma and F-2 – isoprostanes in urine, did not differ by feed or over time. Neither ability to resist oxidative stress/nor RBC superoxide dismutase differed according to feed or over time. CONCLUSION: Data suggest that during erythropoietin therapy antioxidant defence in VLBW infants are capable of dealing with early supplemental iron during treatment with EPO

Available Coal Resoures of the Handshoe 7.5–Minute Quadrangle, Knott County, Kentucky

Coal resources available for mining have been estimated for the Handshoe Quadrangle within the Hazard Coal Reserve District of the Eastern Kentucky Coal Field. Twelve coal beds within the quadrangle are potentially mineable and comprise the basis of these resource estimates. Seven of these beds have been commercially developed, but only four have produced more than 1 million tons: the Tiptop, Hazard No. 8, Hazard No. 4, and Upper Elkhorn No. 3. A computerized Geographic Information System was used to calculate estimates of original, mined-out, and remaining resources, restrictions to mining, and available resources

Available Coal Resources of the Salyersville South 7.5-Minute Quadrangle, Magoffin County, Kentucky

Coal resources available for mining have been estimated for the Salyersville South Quadrangle, which is located in the Licking River Coal Reserve District of the Eastern Kentucky Coal Field. Nine coal beds within the quadrangle are potentially mineable and constitute the basis of these resource estimates. Seven of these beds have been commercially developed, but only five have produced more than 1 million tons: from youngest to oldest, the Skyline A, Lower Broas, Lower Peach Orchard, Middle Peach Orchard, and Upper Peach Orchard. A computerized Geographic Information System was used to calculate estimates of original, mined-out, and remaining resources, as well as restrictions to mining and available resources