Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

Intellectual Property Management and Commercialization of ICAR-CSSRI Technologies for Management of Salt Affected and Waterlogged Soils of India

ICA

Chemical characterization of wet precipitation events and deposition of pollutants in coal mining region, India

The present study investigated the chemical composition of wet atmospheric precipitation in India’s richest coal mining belt. Total 418 samples were collected on event basis at six sites from July to October in 2003 and May to October in 2004 and analysed for pH, EC, F−, Cl−, SO2_ 4 , NO_3 , Ca2+, Mg2+, Na+, K+ and NHþ4 . The average pH value (5.7) of the rainwater of the investigated area is alkaline in nature. However, the temporal pH variation showed the alkaline nature during the early phase of monsoonal rainfall but it trends towards acidic during the late and high rainfall periods. The rainwater chemistry of the region showed high contribution of Ca2+ (47%) and NHþ4 (21%) in cations and SO24_ (55%) and Cl− (23%) in anionic abundance. The high non seas salt fraction (nss) of Ca2+ (99%) and Mg2+ (96%) suggests crustal source of the ions, while the high nss SO24_ (96%) and high SO2_ 4 _ NO_3 _ þ C1__ratio signifying the impact of anthropogenic sources and the source of the acidity. The ratio of SO2_ 4 þ NO_3 _ NHþ4 _ þ Ca2þ_varies from 0.03 to 3.23 with the average value of 0.84 suggesting that Ca2+ and NHþ4 play a major role in neutralization processes. The assessment of the wet ionic deposition rates shows no any specific trend, however Ca2+ deposition rate was highest followed by SO2_ 4 and NH4