Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

A dominance-based rough set approach applied to evaluate the credit risk of sovereign bonds

4OR - Even though sovereign bonds represent low-risk alternatives that give investors a healthy income, the risk assessment process for these bonds is still considered subjective because of the...     

Alkyl metal asymmetric reduction. 11. The reaction of α,β-unsaturated ketones with β-branched trialkylaluminium compounds.

The reduction of a series of α,β-unsaturated ketones has been studied under various experimental conditions, by using β-branched trialkylalanes. Asymmetric induction phenomena are observed when optically active trialkylalanes are used.     

Construction of a singular elliptic-harmonic measure

The authors study an example, suggested by E. De Giorgi, of a second-order uniformly elliptic partial differential operator in divergence form with continuous coefficients on a smooth domain in the plane such that the associated harmonic measure on the boundary is not absolutely continuous with respect to the ordinary surface measure.     

Transition metal-catalysed sequences of nucleophilic addition

Summary In presence of nickel or palladium catalysts, nucleophiles can attack vinylcyclopropanes with concomitant ring cleavage. With palladium catalysts in presence of appropriate substituents the terminal carbon atom of the resulting open chain is able to add to two molecules of a conjugated diene giving rise to long-chain unsaturated compounds.     

Analysis of Organic Compounds in Antarctic Snow and Their Origin

Abstract

Organic compounds extractable with n-hexane were identified and quantitatively determined in pack, surface and deep snow samples taken at different depths and collected at several altitudes above sea level from Antarctica during the 1993/94 Italian expedition. The comparison between the composition of organic compounds in snow and the ones in pack and sea-water samples pointed out that the three matrices substantially contain the same biogenic and anthropogenic organic compounds. The contribution of marine aerosol to organic content in the snow is confirmed by the enrichment ratios calculated for the more representative classes of identified compounds (n-alkanes, phthalates and low molecular weight alkylbenzenes). The changes in the composition of organic compounds in snow as the altitude increases seem to depend on the dimensional spectrum of the aerosol. Thus, smallest particles, richest in surfactant material, reach the highest altitudes.     

Production of metakaolin from industrial cellulose waste

Research focused on the transformation and utilization of industrial wastes into products of commercial interest plays an increasingly important role. Residual pulp can become useful in the manufacture of different materials, providing high value to this waste and reducing its environmental impact when disposed of improperly in the environment. The main constituents of this waste are kaolin and calcium carbonate (CaCO₃). Starting from kaolin, metakaolin can be produced by calcination of the residue at 630?°C for 2?h in a rotary reactor with air flow, followed by solubilization with hydrochloric acid to remove the CaCO₃. The development of technological alternatives aimed at the reuse of certain wastes can result in applications of real economic interest to the chemical industry and ceramics and glass, which is the case in this study. The raw material and metakaolin obtained were analyzed by thermogravimetric analysis and derivative thermogravimetric analysis, X-ray diffraction, and X-ray fluorescence spectroscopy with promising results. This is because metakaolin was obtained free of contamination by other materials.     

A finite element formulation satisfying the discrete geometric conservation law based on averaged Jacobians

In this article, a new methodology for developing discrete geometric conservation law (DGCL) compliant formulations is presented. It is carried out in the context of the finite element method for general advective–diffusive systems on moving domains using an ALE scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles, it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed‐grid counterpart. However, only a few works proposed a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an averaged ALE Jacobians formulation is obtained. This new formulation is applied to the θ family of time integration methods. In addition, an extension to the three‐point backward difference formula is given. With the aim to validate the averaged ALE Jacobians formulation, a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthesis of bifunctional chelating agents based on mono and diphosphonic derivatives of diethylenetriaminepentaacetic acid

Bifunctional chelating agents (BFCAs) are small molecules containing a chelating unit, able to strongly coordinate a metal ion, and a reactive functional group, devised to form a stable covalent bond with another molecule. BFCAs are widely employed since their conjugation to a suitable biomolecule (e.g., a peptide or an antibody) allows the synthesis of diagnostic or therapeutic agents that specifically target diseased tissue with metals or radiometals. For this reason, BFCAs find application in diagnostic imaging, molecular imaging, and radiotherapy of cancer. The synthesis of new BFCAs based on a diethylenetriaminepentaacetic acid (DTPA) structure in which one or two carboxylic groups are replaced with phosphonic units is described. The phosphonic group, aside from being a classical isostere of the carboxylic acid in coordination chemistry, allows to modulate the physico-chemical properties of the ligands and of the corresponding complexes.