The evaluation of Cauchy principal value integrals involving unknown poles

A method is described for the evaluation of a Cauchy principal value integral of the formf ₀ ^p f(t)dt, wheref is analytic in the interval [0,p] except at a simple pole at an unknown point in (0,p), with an unknown residue. The method is based on the trapezoidal rule.     

ZurL 2-Bestapproximation eines konvexen Körpers durch einen bewegten konvexen Körper

LetK andL be convex bodies of then-dimensional Euclidean spaceE ⁿ . The -distance ofK andL is defined by , whereh _k andh _L denote the support functions ofK andL restricted to the unit sphereS ^n–1 E ⁿ . We consider the problem of best approximation ofL by the images k ofK under proper rigid motions :E ⁿ E ⁿ . A motion that minimizes ²(K L) is called optimal for (K, L) in the sense of the metric ². The results in the general case (n2 arbitrary) base on the fact that the Steiner points of K andL coincide if is optimal for (K, L). Forn=2 we obtain a relationship between convex convolution bodies and the underlying approximation problem.     

Geometric techniques in representation theory

A discussion of results and conjectures, focussed around the extension of the modular representation theory for finite Lie-type groups to more general groups that act on building-like geometries.Based on a lecture given at the conference Groups and Geometries-Finite and Algebraic, on 26 March 1986 at Noordwijkerhout, Netherlands (a NATO Advanced Research Workshop).Partially supported by NSF Grant MCS 83-00855.     

Separation and analysis of radioiodine in nuclear reprocessing solutions of high ionic strength

Ion chromatography (IC) can be used to separate radioiodine from fission products and other ionic species in complex reprocessing solution matrices. A preliminary concentration and separation of the radioiodine is performed using a column filled with a platinum-coated copper bed which converts all forms of iodine to iodide and selectively adsorbs the iodide. The separation is completed by employing an anion chromatographic system. The iodide peak aliquot is collected for subsequent radioanalysis by low energy photon spectroscopy. Results indicate quantitative separation and recovery of iodine. The entire system is automated under computer control and is able to handle small (l) and large (500 ml) sample sizes.