Determination of trialkyllead species in water samples

An analytical compound procedure is described for the determination of trimethyl- and triethyllead in water samples like rain, melted snow, and surface waters. The method consists of an enrichment step (adsorption onto and elution from silica gel), a chromatographic separation with column switching (HPLC including pre-column enrichment), and a spectrophotometric detection (chemical reaction detector). The detection limits for the whole procedure, starting with 500 ml sample volume, are 15 pg/ml and 20 pg/ml for trimethyl- and triethyllead resp. The standard deviation for repeated analysis of a sample containing 90 pg Et3Pb+/ml is calculated to +/- 4%. The method also covers the analysis of the chemically mixed trialkyllead species Me2EtPb+ and MeEt2Pb+. The investigation of several water samples taken from different locations shows the presence of trimethyl- and triethyllead in the concentration range of 20-100 pg/ml.     

The decomposition numbers of the hecke algebra of typeF 4

LetW be the finite Coxeter group of typeF ₄, andH _r (q) be the associated Hecke algebra, with parameter a prime powerq, defined over a valuation ringR in a large enough extension field ofQ, with residue class field of characteristicr. In this paper, ther-modular decomposition numbers ofH _R (q) are determined for allq andr such thatr does not divideq. The methods of the proofs involve the study of the generic Hecke algebra of typeF ₄ over the ringA = ℤ[u ^1/2,u ^-1/2] of Laurent polynomials in an indeterminateu ^1/2 and its specializations onto the ring of integers in various cyclotomic number fields. Substancial use of computers and computer program systems (GAP, MAPLE, Meat-Axe) has been made.     

Constraint Programming Based Lagrangian Relaxation for the Automatic Recording Problem

Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the merits of both approaches. We introduce a general way of how linear optimization constraints can strengthen their propagation abilities via Lagrangian relaxation. The method is evaluated on a set of benchmark problems stemming from a multimedia application. The experiments show the superiority of the combined method compared with a pure OR approach and an algorithm based on two independent optimization constraints.