Small Data Scattering for the Nonlinear Schrödinger Equation on Product Spaces

We consider the cubic nonlinear Schrödinger equation, posed on ? ⁿ  × M, where M is a compact Riemannian manifold and n ≥ 2. We prove that under a suitable smallness in Sobolev spaces condition on the data there exists a unique global solution which scatters to a free solution for large times.     

A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Nanoporous oxide formation by anodic oxidation of Nb in sulphate–fluoride electrolytes

The influence of hydrofluoric acid (HF) concentration and applied potential on the processes of anodic oxidation of Nb in sulphuric acid solution was studied by chronoamperometry, electrochemical impedance spectroscopy and scanning electron microscopy. During the first stage of the process, a compact barrier film is formed. On top of this film, a porous overlayer starts to form, then the nanopores grow into an ordered nanostructure. Subsequently, secondary 3D flower-shaped structures begin to form. These structures gradually spread all over the surface as an irregular multilayer film. The rates of the process of porous overlayer formation and subsequent growth of nanopore arrays increase with applied potential as well as with the HF concentration. The films have been characterised ex situ by electrochemical impedance spectroscopy at open circuit potential and capacitance vs. potential measurements to follow the different stages of nanoporous film formation with electrochemical methods. The impedance spectra and capacitance vs. potential curves have been interpreted using previously proposed models for the amorphous semiconductor/electrolyte interface. An attempt to rationalise the mechanism of nanoporous layer growth is presented by using the conceptual views of the mixed-conduction model and recent ideas for porous film formation on valve metals.     

Strichartz estimates for the periodic non-elliptic Schrödinger equation

The purpose of this Note is to prove sharp Strichartz estimates with derivative losses for the non-elliptic Schrödinger equation posed on the 2-dimensional torus.     

Effect of silver modification on structure and catalytic performance of Ni-Mg/diatomite catalysts for edible oil hydrogenation

Silver modified Mg-Ni/diatomite materials with ratios of SiO₂/Ni = 1.07 and Mg/Ni = 0.1, differing in Ag content (Ag/Ni = 0.025 and 0.1) were prepared by the precipitation–deposition method. The effects of silver presence and content on the structure, morphology, texture and H₂-adsorption capacity of the obtained precursors were studied by X-ray diffraction, scanning electron microscopy, Hg-porosimetry and H₂-chemisorption techniques. The catalytic performance of the corresponding catalysts in the soybean oil hydrogenation was investigated. The increase of the silver loading resulted in the development of macroporosity and increase in the total sample porosity. The decrease of both H₂-adsorption capacity and hydrogenation activity are related to the metallic silver covering and blocking effects on the Ni²⁺ species, thus hampering the access of hydrogen. The decrease of hydrogenation activity and favorable limiting of cis–trans isomerization on the silver modified catalyst are explained by Horiuti–Polanyi mechanism based on the assumption that hydrogenation and isomerization proceed at the same active metallic nickel sites via half-hydrogenated intermediates.It was shown that the adjustment of the catalyst composition by changing the content of silver modifier offers the possibility to control the total amount of solid fat content, stearic acid and detrimental trans fatty acids in the hydrogenated derivatives. The catalyst with higher silver content is proposed as a promising candidate for selective edible oil hydrogenation catalyst.     

Genome-wide single-nucleotide polymorphism arrays demonstrate high fidelity of multiple displacement-based whole-genome amplification

Whole-genome DNA amplification by multiple displacement (MD-WGA) is a promising tool to obtain sufficient DNA amounts from samples of limited quantity. Using Affymetrix' GeneChip Human Mapping 10K Arrays, we investigated the accuracy and allele amplification bias in DNA samples subjected to MD-WGA. We observed an excellent concordance (99.95%) between single-nucleotide polymorphisms (SNPs) called both in the nonamplified and the corresponding amplified DNA. This concordance was only 0.01% lower than the intra-assay reproducibility of the genotyping technique used. However, MD-WGA failed to amplify an estimated 7% of polymorphic loci. Due to the algorithm used to call genotypes, this was detected only for heterozygous loci. We achieved a 4.3-fold reduction of noncalled SNPs by combining the results from two independent MD-WGA reactions. This indicated that inter-reaction variations rather than specific chromosomal loci reduced the efficiency of MD-WGA. Consistently, we detected no regions of reduced amplification, with the exception of several SNPs located near chromosomal ends. Altogether, despite a substantial loss of polymorphic sites, MD-WGA appears to be the current method of choice to amplify genomic DNA for array-based SNP analyses. The number of nonamplified loci can be substantially reduced by amplifying each DNA sample in duplicate.     

Random data Cauchy theory for supercritical wave equations I: local theory

We study the local existence of strong solutions for the cubic nonlinear wave equation with data in H ^s (M), s<1/2, where M is a three dimensional compact Riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in H ^s (M), where s≥1/4 in the case of a boundary less manifold and s≥8/21 in the case of a manifold with boundary. Mathematics Subject Classification (2000)  35Q55, 35BXX, 37K05, 37L50, 81Q20