Preconcentration of mercury using duolite GT-73 in the analysis of water samples by inductively coupled plasma atomic emission spectrometry.

Duolite GT-73 resin was used for the preconcentration of Hg(II) from hydrochloric acid media as well as separation of the analyte from diversity of the co-existing metal ions (Al, Ca, Cd, Co, Cr, Cu, Fe, Mg, Mn, Ni, Pb and Zn) in off-line column operation. Due to the high affinity of the resin to the transition metals, Hg was adsorbed alongside with the foreign metals investigated. A complete release of the concomitant metals from the resin without the desorption of Hg was carried out using solutions of HCl and HNO3. A quantitative recovery of Hg was obtained by digestion of the resin using a H2SO4 and H2O2 mixture in an open-vessel system. An enrichment factor of 40 was achieved. The devised procedure was applied for the determination of Hg(II) in tap-water samples.     

Derivatization of 1-phenyl substituted 4-amino-2-benzazepin-3-ones: evaluation of Pd-catalyzed coupling reactions

Several Pd-catalyzed reactions were explored to further functionalize the bromo-substituted 4-amino-1,2,4,5-tetrahydro-2-benzazepin-3-one scaffold (Aba). We report in this paper suitable reaction conditions for Suzuki, Buchwald-Hartwig, and Heck reactions. The substitution pattern of the starting aminobenzazepinone turned out to be crucial for the success of these transition metal-catalyzed reactions, which often required modifications of standard literature procedures. The Pd-catalyzed methods provide access to novel substitution patterns of the Aba scaffold.     

Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.