Progress in the quality assurance of environmental trace organic analysis

An overview is given on the stepwise learning programmes undertaken to identify the main sources of error associated with the determination of the mandatory organic contaminants in the marine monitoring programmes. Details are given on the preparation and use of LRMs and CRMs to maintain analytical control and quantify the laboratory errors in relation to the measurement of changes in the environment.     

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The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

The emergence of a giant component in random subgraphs of pseudo‐random graphs

Let G be a d‐regular graph G on n vertices. Suppose that the adjacency matrix of G is such that the eigenvalue λ which is second largest in absolute value satisfies λ = o(d). Let G_p with p = α/d be obtained from G by including each edge of G independently with probability p. We show that if α < 1, then whp the maximum component size of G_p is O(log n) and if α > 1, then G_p contains a unique giant component of size Ω(n), with all other components of size O(log n). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Promiscuity in Antibody Catalysis: Esterolytic Activity of the Decarboxylase 21D8

The high structural similarity of decarboxylase antibody 21D8 and esterase antibody 48G7 suggests that 21D8 might also possess hydrolytic activity. Kinetic investigations show that 21D8 does promote the selective hydrolysis of methyl 4‐nitrophenyl carbonate and sodium 4‐(acetoxy)benzenesulfonate with catalytic proficiencies (k_cat/K_m)/k_un of ca. 10⁵ M ^?1. The ability of 21D8 to accelerate a reaction for which it was not developed suggests that certain antibody scaffolds are intrinsically predisposed toward catalysis, a property that can be enhanced and refined during affinity maturation in response to a transition‐state analog. At the same time, however, the restricted structural diversity of the immune system may ultimately limit the catalytic efficiency that can be achieved.     

Some New uniform frames with block size four and index one or three

In this paper, some new uniform frames with block size four and index one or three are obtained. The known existence results for (4,1)‐frames and (4,3)‐frames are both improved to the extent that only a finite number of possible exceptions remain. © 2003 Wiley Periodicals, Inc.     

Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (₀ F ₁) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these ₀ F ₁functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( _r F _s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP₂properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866).