Baseline Methods for Bayesian Inference in Gumbel Distribution

Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.     

New mass spectrometric approaches to structural analysis in mixtures

Structural analysis of minor components in mixtures is a vital requirement in the development of any pharmaceutical compound. Mass spectrometry is uniquely able to give this kind of information on the trace amounts of material present as minor impurities in a drug substance. In this study we show that a combination of mass spectrometric analysers with different characteristics is an even more powerful approach with a higher chance of establishing a potential structure. In particular the advent of analysers capable of accurate mass measurement on small amounts of material has enabled structures to be proposed in situations where previously no real conclusions could be made. Copyright 1999 John Wiley & Sons, Ltd.     

Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients

In this paper the exact solution of the non-symmetric matrixRiccati equation with analytic coefficients is approximatedby a rational matrix function with a prefixed accuracy. Thisrational matrix function is locally defined as the exact solutionof a Riccati problem with matrix polynomial coefficients obtainedby truncation of the Taylor expansions of the matrix coefficientsof the original problem.     

M(C6H16N3)2(VO3)4 as heterogeneous catalysts. Study of three new hybrid vanadates of cobalt(II), nickel(II) and copper(II) with 1-(2-aminoethyl)piperazonium

Three new hybrid vanadates have been synthesized under hydrothermal conditions with the formula M(C(6)H(16)N(3))(2)(VO(3))(4), where M = Co(II), Ni(II) and Cu(II). The structural analyses show that the phases are isostructural and crystallize in the monoclinic space group P2(1)/c. These compounds show a two-dimensional crystal structure, with sheets composed of [VO(3)](n)(n-) chains and metal centres octahedrally coordinated, chelated by two 1-(2-aminoethyl)piperazonium ligands. The thermal study reveals that the copper containing phase is less stable than the cobalt and nickel containing ones. The IR spectra of the three phases are very similar, with little differences in the inorganic bond region of the copper containing phase. The UV-visible spectra show that the cobalt(II) and the nickel(II) are in slightly distorted octahedral environments. The catalytic tests show that the phases act as heterogeneous catalysts for the selective oxidation of alkyl aryl sulfides, with both H(2)O(2) and tert-butylhydroperoxide as oxidizing agents. The influence of the steric hindrance in the kinetic profile has been studied. The catalytic reactions induce the partial amorphization of the phases.     

Numerical continuation of degenerate homoclinic orbits in planar systems

In this paper we develop numerical algorithms for the continuationof degenerate homoclinic connections in planar systems. We considerthe case where the equilibrium point has zero trace and twocases of higher-order degeneracies. The method we propose isable to continue homoclinic connections of order up to codimension-four.Application of the algorithm to four examples supports its validityand demonstrates its usefulness.     

Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.