Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

A confidence interval for the slope of a truncated regression

Summary Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = _o X + V subjected to the truncationYy ₀. The estimate corresponds to the zero-crossing of a random functionS _n (). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS _n () in the neighborhood of the true value _o.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.     

Haplotyping by capillary electrophoresis

The investigation of the genetic background and phenotype structures of complex diseases, such as cardiovascular or psychiatric disorders and tumors, is one of the most scrutinized fields of the post genomic era. Besides the multiplex analysis of genetic markers and polymorphisms throughout the whole genome, more and more attention is focused on the interaction between the etiological factors of these traits. Haplotype determination, rather than multiplex genotyping seems to be one of the first building blocks of this endeavor. This review focuses on the importance and theoretical background of haplotyping, and summarizes the recent examples of novel and emerging haplotyping techniques by capillary gel electrophoresis based DNA fragment analysis, a powerful tool for the examination of the inheritance of complex traits.     

Adducts of Rh2[MTPA]4 with some phosphine chalcogenides: nature of binding and ligand exchange

Adducts of four phosphine chalcogenides with the chiral dirhodium complex ([Rh-Rh]) were investigated by variable-temperature 1H and 31P NMR spectroscopy in order to compare their properties as axial ligands. Whereas the selenide (1) and the sulfide (2) are strong ligands with electrostatic attraction and, in addition, a significant orbital (HOMO-LUMO) interaction, the phosphine oxide compounds (P=O) bind primarily via electrostatic attraction and are relatively weak donors. Moreover, the overall bond strength in these adducts depends on steric congestion around the P=O group.     

Speciation in the aqueous H+/H2VO4-/H2O2/picolinate system relevant to diabetes research

A detailed study of the quaternary aqueous H+/H2VO4-/H2O2/picolinate (Pi-) system has been performed at 25 degrees C in 0.150 M Na(Cl) medium using quantitative 51 V NMR (500 MHz) and potentiometric data (glass electrode). In the ternary H+/H2VO4-/Pi- system, six complexes have been found in the pH region 1-10. In the quaternary H+/H2VO4-/H2O2/Pi- system, eight additional complexes have been found. Generally, equilibria are fast in both systems. The rate of peroxide decomposition depends on the species in solution. Chemical shifts, compositions and formation constants for the species are given. Equilibrium conditions and the fit of the model to the experimental data are illustrated in distribution diagrams. Possible formation of mixed ligand species with imidazole, lactic acid and citric acid have been investigated and ruled out under the same experimental conditions. Structural proposals are given, based on 1)C NMR data and available crystal structures.     

Unexpected ring transformation to pyrrolo[3.2-b]pyridine derivatives. Fused azolium salts. 22

2-Arylsulfanyl and 2-benzylsulfanylpyridinium N-arylimides (2) easily prepared from 3-aryltetrazolopyridinium salts (1) with aryl and benzylthiolates, respectively, reacted with various dipolarophiles yielding cycloadducts that underwent transformation to give tetrahydropyrrolo[3,2-b]pyridines (5, 6, and 8) in good yields. A similar rearrangement (formation of 15) was also observed in the case of parent derivatives being unsubstituted in position 2 (12). The abscence of any significant solvent effect, comparison of the sulfur and non-sulfur analogues, as well as the stereoselective nature of the observed ring transformation seem to support a sigmatropic mechanism. Structure elucidation of the products has been carried out by single-crystal X-ray diffraction and (1)H NMR experiments.     

Accreditation of reference material producers: the example of IRMM's Reference Materials Unit

The potential approaches for third-party assessment of reference material producers are revisited and the activities of the Reference Materials (RM) Unit of the Institute for Reference Materials and Measurements (IRMM) to obtain accreditation to ISO Guide 34 and ISO 17025 are described. Accreditation was related to the Unit as all matrix RM activities of the institute are concentrated there. A management system was established that allows sufficient flexibility to be applicable to a wide range of RMs while being precise enough to ensure compliance with ISO Guides 30, 31 and especially 34 and 35. Accreditation was achieved in 2004 with independent scopes for testing and RM production and was confirmed and extended in 2005. The key aspects of the RM Unit's management system for RM production are presented. Presented at BERM-10, April 2006, Charleston, SC, USA