An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem

Summary. This paper is concerned with a high order convergent discretization for the semilinear reaction-diffusion problem: , for , subject to , where . We assume that on , which guarantees uniqueness of a solution to the problem. Asymptotic properties of this solution are discussed. We consider a polynomial-based three-point difference scheme on a simple piecewise equidistant mesh of Shishkin type. Existence and local uniqueness of a solution to the scheme are analysed. We prove that the scheme is almost fourth order accurate in the discrete maximum norm, uniformly in the perturbation parameter . We present numerical results in support of this result. Received February 25, 1994     

Einige Bemerkungen zum Vierscheitelsatz

Zusammenfassung. Der Vierscheitelsatz sagt aus, da? die Krümmung einer geschlossenen, sich selbst nicht schneidenden, ebenen Kurve stets mindestens zwei Maxima und zwei Minima besitzt. Er wurde unabh?ngig von Syamadas Mukhopadhyaya und von Adolf Kneser bewiesen, und seitdem hat es eine ganze Reihe weiterer Beweise gegeben. In der vorliegenden Note wird der Satz aus einer elementargeometrischen Aussage über Kreisbogenvielecke durch Grenzübergang hergeleitet und schlie?lich durch Abschw?chung der Differenzierbarkeitsvoraussetzungen verallgemeinert. Eingegangen am 13. Dezember 1994 / Angenommen am 3. M?rz 1995     

Pentopyranosyl Oligonucleotide Systems. 9th Communication

Pyranosyl‐RNA (‘p‐RNA’ ) is an oligonucleotide system isomeric to natural RNA and composed of the very same building blocks as RNA. Its generational, chemical, and informational properties are deemed to be those of an alternative nucleic acid system that could have been a candidate in Nature's evolutionary choice of the molecular basis of genetic function. We consider the study of the chemistry of p‐RNA as etiologically relevant in the sense that knowledge of its structural, chemical, and informational properties on the chemical level offers both a perspective and reference points for the recognition of specific structural assets of the RNA structure that made it the (supposedly) superior system among possible alternatives and, therefore, the system that became part of biology as we know it today. The paper describes the chemical synthesis of β‐d‐ (and L )‐ribopyranosyl‐(4′→2′)‐oligonucleotide sequences, presents a resume of their structural and chemical properties, and cautiously discusses what we may and may not have learned from the pyranosyl isomer of RNA with respect to the conundrum of RNA's origin.     

Common luminescence intensity fluctuations of single particle and single molecules in non-conducing matrices

Optical spectroscopy in combination with wide field or confocal optical microscopy enables the investigation of single quantum objects such as organic molecules, II/VI semiconductor quantum dots and silicon nanocrystals. They all have fluctuations of luminescence intensities on time scales longer than μs in common. A comparison reveals that despite the large differences of the nature of the respective quantum objects, the intensity fluctuations are related to a slow ionisation process followed by a trapping of the photoejected charge in the non-conducing environment. Detailed aspects of the dynamics are controlled by the dielectric properties of the matrix.     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Foams and surface rheological properties of β-casein, gliadin and glycinin

Interfacial rheological properties and their suitability for foam production and stability of two vegetable proteins were studied and compared to β-casein. Proteins used ranged from flexible to rigid/globular in the order of β-casein, gliadin and soy glycinin. Experiments were performed at pH 6.7. Network forming properties were characterised by the surface dilational modulus (determined with the ring trough) and the critical falling film length (L_still) at which a stagnant protein film will break. Gliadin had the highest dilational modulus, followed by glycinin and β-casein, whereas glycinin formed the strongest film against fracture in the overflowing cylinder. The rate of decrease in the surface tension was studied at the air–water (Wilhelmy plate method) and the oil–water interface (bursting membrane) and the dynamic surface tension during compression and expansion in the caterpillar. Gliadin had the lowest equilibrium interfacial tensions and β-casein the lowest dynamic surface tension during expansion. Hardly any foam could be formed at a concentration of 0.1 g/l by shaking. At a concentration of 1.4 g/l most foam was formed by β-casein, followed by gliadin and glycinin. It seems that in the first place the rate of adsorption is important for foam formation. For the vegetable proteins, adsorption was slow. This resulted in lower foamability, especially for glycinin.     

Vapor-liquid equilibrium data at 25°C for six binary systems containing methyl acetate or methanol,with dichloromethane,chloroform, or 1,2-trans-dichloroethylene

Isothermal vapor-liquid equilibrium (VLE) data, at 25° C were determined by a saturation method for each of the six methanol or methyl acetate binary systems with dichloromethane, chloroform, and 1,2-trans-dichloroethylene. The experimental data satisfy the Redlich-Kister consistency test, and were correlated with five Gibbs free energy models. All the binary mixtures of methanol with the chlorinated compounds exhibit strong positive deviations from ideality while the mixtures of methyl acetate with the chlorinated compounds present negative deviations from ideal behavior.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Matrix effects in the determination of butyltin compounds in environmental samples by GC AA after hydride generation

Experiments for the determination of mono-, di and tri-butyltin (MBT, DBT and TBT) by hydride generation/gas chromatography/atomic absorption spectrometry in various matrices (sediment, suspended matter, mussel, algae and water) have revealed that poor butyltin recoveries are obtained in sediments displaying high sulphur and hydrocarbon contents; very poor recoveries were also observed for TBT in sediments with high chlorophyll pigment contents as well as in algal samples. It was however not clear whether the hydride generatin was inhibited by these infering compounds, as was previously assumed in the case of hydrocarbons, or whether interferences affected the atomization rate. Further studies were performed to solve this problem in order to validate this method in the case of analyses of, for example, oil-contaminated sediment and algae. This paper presents the results obtained. It is concluded here that the poor recoveries were due to an inhibition of hydride generation rather than to interference at the atomization stage.