Determination of thorium and uranium at the nanogram per gram level in semiconductor potting plastics by neutron activation analysis

A method was developed to determine thorium and uranium in semiconductor potting plastics. The method is based on neutron activation and subsequent radiochemical separation to isolate and permit measurement of the daughter products²³³Pa and²³⁹Np of the induced²³³Th and²³⁹U. These plastics typically contain macro amounts of silicon, bromine and antimony and nanogram per gram amounts of thorium and uranium. The radiochemical method provides the necessary sensitivity and makes it possible to easily attain adequate decontamination of the tiny amounts of²³³Pa and²³⁹Np from the high levels of radioactive bromine and antimony.Deceased     

Squalestatin alters the intracellular trafficking of a neurotoxic prion peptide

Background  

Neurotoxic peptides derived from the protease-resistant core of the prion protein are used to model the pathogenesis of prion diseases. The current study characterised the ingestion, internalization and intracellular trafficking of a neurotoxic peptide containing amino acids 105–132 of the murine prion protein (MoPrP105-132) in neuroblastoma cells and primary cortical neurons.     

A geometric approach to complete reducibility

Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert–Mumford–Kempf from geometric invariant theory. We deduce that a normal subgroup of a G-completely reducible subgroup of G is again G-completely reducible, thereby providing an affirmative answer to a question posed by J.-P. Serre, and conversely we prove that the normalizer of a G-completely reducible subgroup of G is again G-completely reducible. Some rationality questions and applications to the spherical building of G are considered. Many of our results extend to the case of non-connected G. Mathematics Subject Classification (2000) 20G15, 14L24, 20E42     

The Besicovitch–Federer projection theorem is false in every infinite-dimensional Banach space

The theme of the article is the study of the unipotent part of Arthur’s trace formula for general linear groups. The case of regular (or “regular by blocks”) unipotent orbits has been treated in another paper (cf. [10]). Here we are interested in the contribution of Richardson orbits that are induced by Levi subgroups with two-by-two distinct blocks. In this case, the contribution is remarkably given by a global unipotent weighted orbital integral. As a corollary, we get integral formulas for some of Arthur’s global coefficients. We also present a new construction of Arthur’s local unipotent weighted orbital integral and an explicit computation of some of them.     

Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras

Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G ⁿ , the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic characterization of the closed H-orbits in G ⁿ , generalizing work of Richardson which treats the case H = G. This characterization turns out to be a natural generalization of Serre??s notion of G-complete reducibility. This concept appears to be new, even in characteristic zero. We discuss how to extend some key results on G-complete reducibility in this framework. We also consider some rationality questions.     

Reliability in scientific evidence based on multi trace forensic neutron activation analysis

The forensic activation analyst must often evaluate his own results as they relate to certain legal or moral situations, since investigative officers, and courts of law are not usually competent to make judgements of the validity or meaning of scientific data. In providing scientific evidence in court, two criteria for criminal identification must be met: (1) suspect's sample should be similar to sample found at the scene of the crime, (2) samples relared to other people in the same statistical population should not generally match that found at the crime site. When two or more specimens are submitted for comparison by NAA they will usually fall into one of three classes: (a) materials about which we have partial or inconclusive data, (c) materials with an excellent analytical data background. Ideally all cases would fall in category c; in practice, very few. Some examples of cases and/or situations that fall into these three categories in both individual and corporate investigations are given. Research sponsored by U.S. Atomic Energy Commission under contract with Union Carbide Corporation.     

Complete reducibility and separable field extensions

Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies on the recently established Tits Centre Conjecture for the spherical building of the reductive group G.     

On a question of Külshammer for representations of finite groups in reductive groups

Let G be a simple algebraic group of type G₂ over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ₂ and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ₂ are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H¹(Γ, V) → H¹(Γ_p, V) induced by restriction of 1-cocycles has an infinite fibre.