Reliable Solution of Bidiagonal Systems with Applications

We show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems.     

Deterministic Percolation

This paper examines percolation questions in a deterministic setting. In particular, I consider , the set of elements of Z ² with greatest common divisor equal to 1, where two sites are connected if they are at distance 1. The main result of the paper proves that the infinite component has an asymptotic density. An “almost everywhere” sieve of J. Friedlander is used to obtain the result. Received: 1 November 1998 / Accepted: 1 April 1999     

Biological control of fungal pathogens

Biological control of soil-borne plant pathogens is a potential alternative to the use of chemical pesticides, which have already been proved to be harmful to the environment. Several strains of the fungusTrichoderma have been isolated and found to be effective biocontrol agents of various soil-borne plant pathogenic fungi under greenhouse and field conditions. Different application approaches have been used including integration ofTrichoderma with reduced doses of chemical agents. Biochemical and molecular biology studies carried out to explore the mechanisms involved in biological control revealed thatTrichoderma is a rather specific mycoparasite. Lectins were found to be involved in the recognition betweenTrichoderma and its host fungi, whereas chitinase is involved in the degradation of the host cell wall. Genetic engineering techniques were employed in order to increase the effectiveness, stability, and biocontrol capacity ofTrichoderma spp. as well as other biocontrol agents, such asPseudomonass spp. andRhizobium.     

Hydrogen bond dynamics at water/organic liquid interfaces

Hydrogen bond dynamics at the neat interface between water and a series of organic liquids are studied with molecular dynamics computer simulation. The organic liquids are nonpolar (carbon tetrachloride), weakly polar (1,2-dichloroethane), and polar (nitrobenzene). The effect of surface polarity and surface roughness is examined. The dynamics are expressed in terms of the hydrogen bond population autocorrelation functions and are found to be nonexponential and strongly dependent on the nature of the organic phase. In particular, at all interfaces, the dynamics are slower at the interface than in the bulk and sensitive to the location of the water molecules along the interface normal.     

New algorithms for polynomial and trigonometric interpolation on parallel computers

An interpolation polynomial of orderN is constructed fromp independent subpolynomials of ordern N/p. Each such subpolynomial is found independently and in parallel. Moreover, evaluation of the polynomial at any given point is done independently and in parallel, except for a final step of summation ofp elements. Hence, the algorithm has almost no communication overhead and can be implemented easily on any parallel computer. We give examples of finite-difference interpolation, trigonometric interpolation, and Chebyshev interpolation, and conclude with the general Hermite interpolation problem.     

Stereospecific nucleophilic substitution at tertiary and quaternary stereocentres

Nucleophilic substitution reactions have always been considered as one of the most powerful reactions for the creation of carbon–carbon or carbon–heteroatom bonds in organic synthesis. In contrast to secondary carbons, the steric shielding of tertiary carbons retards a concerted, stereospecific nucleophilic substitution, and ionizing pathways often lead to nonselective substitution due to ion pair dissociation. In this minireview, we will detail pioneering contributions and more recent achievements emphasizing the feasibility of nucleophilic substitution on tertiary stereocentres under certain conditions, with inversion of configuration. The development of these transformations at tertiary centres are of remarkable added value to practitioners in the field of complex molecule synthesis. A stereoselective substitution at a quaternary carbon stereocentre with inversion of configuration is also discussed in the case of a three-membered ring.

In this minireview, we summarized the fascinating and rich area of stereoselective or stereospecific nucleophilic substitution at tertiary and quaternary carbon centres.     

Electron impact ionization of unstable enols: H2CCHOH,H2CC(OH)?CH3 and H2CC(OH)?C2H5

Ethenol, 2-hydroxypropene and 2-hydroxybutene-1 were prepared by low-pressure pyrolysis of cyclobutanol, 1-methylcyclobutanol and 1-ethylcyclobutanol, respectively. Mass spectra, ionization energies, appearance energies of metastable ions and kinetic energy releases were determined on a reverse Nier-Johnson double-focusing mass spectrometer. Mercury and CH₃ radicals from the pyrolysis of dimethylmercury were employed for calibration of the energy scale. The ionization energy of 2-hydroxybutene-1 is 8.55 ± 0.1 eV and the appearance energies of [C₂H₅CO]⁺ and [CH₃CO]⁺ from that molecule are 10.25 ± 0.1 and 10.40 ± 0.1 eV, respectively. Changes observed in metastable peak shapes for certain fragmentation reactions upon pyrolysis are discussed.     

The use of tin-decorated mesoporous carbon as an anode material for rechargeable lithium batteries

A sonochemical process has been developed for the insertion of tin nanoparticles into mesoporous carbon, giving a product which was used as a building block for the anode of a rechargeable Li battery; the electrode could deliver a reversible capacity of 400 mAh gr(-1)(C + Sn) at 100% cycling efficiency, which is higher than that of graphite electrodes.