On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Norm-graphs and bipartite turán numbers

For everyt>1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|c _t ·n ^2–1/t which do not contain a complete bipartite graghK _t,t !+1 This establishes the exact order of magnitude of the Turán numbers ex (n, K _t,s ) for any fixedt and allst!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.Research supported in part by NSF Grants DMS-8707320 and DMS-9102866.Research supported in part by Hungarian National Foundation for Scientific Research Grant     

Simultaneous determination of propranolol and pindolol by synchronous spectrofluorimetry

A completely automated method to determine the most common parameters in cured meat products is proposed. The approach to full automation is based on the coupling of a robotic station for development of preliminary operations (namely weighing of the sample, grinding, leaching, filtration and transport to the aspiration zone) and a continuous unsegmented manifold for derivatisation and spectrophotometric monitoring of the reaction coloured products. This assembly works in an unattended fashion thus eliminating the bottleneck produced by the determination of these parameters in routine laboratories. The good agreement between results obtained by the proposed method and those from conventional methods for target analytes confirms its excellent performance and usefulness.     

Synthesis and structure of a dithioether-substituted butene-2-olide-4-ylidene-4 cobalt carbonyl complex

The complex (1) has been prepared and its structure determined. Complex1 is the first stable thioether derivative of a metal carbonyl containing only cobalt as metal. It crystallizes in the monoclinic P2₁/c space group, witha = 13.975( 4 ),b = 11.363( 3 ),c = 14.686(2)A, = 112.25(2)°,V = 2158.5(7)A³.Z = 4. The solution using direct methods and the anisotropic refinement of all nonhydrogen atoms led toR = 0.039,wR = 0.041 for 3296 reflections with F> 4.0(F) Analogous but less stable complexes are formed with 1,6-diphenyl-2,5-dithiahexane and the crown thioether 1,4,7-trithiacyclonane, the latter functioning either as a bidenlate or a tridentate ligand.     

Space and time-resolved laser-induced breakdown spectroscopy using charge-coupled device detection

Space and time-resolved studies of laser induced plasmas in air at atmospheric pressure are presented. Photovoltaic solar cells have been used as samples. The second harmonic (532 nm) of a Nd : YAG laser at an irradiance of 18 x 10(12) W/cm(2) has been used. The precise focus of the beam allows a microanalysis at a 0.02 mm(2) surface area working in single-shot mode. The use of an intensified charge-coupled device (CCD) detector has allowed time-resolved studies in both imaging or spectroscopy modes. The two-dimensional capability of the CCD has enabled the study of atomic and ionic species distribution along the plume. Most data have been recorded using single-laser shot experiments. Spectral lines have been assigned to transitions in atomic components of the material under investigation in the neutral or ionic states of the corresponding atoms. Effects of delay in improving spectral resolution and some examples of spectral characterization of species as a function of its decay are shown.     

Synthesis of Enantiopure Primary Amines by Stereoselective Ring Opening of Chiral Octahydro-1,3-benzoxazines by Grignard and Organoaluminum Reagents

Chiral 1,3-perhydrobenzoxazines 1, 2, and 9-14, prepared by condensation of 8-(benzylamino)menthol with different aldehydes, react with alkylmagnesium bromides and trimethylaluminum leading to the open amino alcohols 3a-d, 4a-d, and 15-20 in excellent chemical yields and good to excellent diastereomeric excess. The sequential elimination of the menthol appendage by heating with P(2)O(5) and the benzyl group by hydrogenolysis lead to primary amines 7a-d, 8a-d, and 27-30 in excellent chemical yields and ee. The addition of the alkyl group from the Grignard derivatives and the methyl group from the trimethylaluminum occurs from opposite sides of the heterocycle, yielding the final primary amines with the same stereochemistry.