Criteria for Pointwise Growth and Their Role in Invasion Processes

This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of singularities of the pointwise Green’s function and pinched double roots of the dispersion relation. The primary aim of this work is to establish some rigorous properties related to these criteria and the relationships between them. In the process, we discover that these concepts are not equivalent and point to some interesting consequences for nonlinear front invasion problems. Among the more striking is the fact that pointwise growth does not depend continuously on system parameters. Other results include a determination of the circumstances under which pointwise growth on the real line implies pointwise growth on a semi-infinite interval. As a final application, we consider invasion fronts in an infinite cylinder and show that the linear prediction always favors the formation of stripes in the leading edge.     

Synthesis of Galactosyl‐Queuosine and Distribution of Hypermodified Q‐Nucleosides in Mouse Tissues

Queuosine (Q) is a hypermodified RNA nucleoside that is found in tRNA^His, tRNA^Asn, tRNA^Tyr, and tRNA^Asp. It is located at the wobble position of the tRNA anticodon loop, where it can interact with U as well as C bases located at the respective position of the corresponding mRNA codons. In tRNA^Tyr and tRNA^Asp of higher eukaryotes, including humans, the Q base is for yet unknown reasons further modified by the addition of a galactose and a mannose sugar, respectively. The reason for this additional modification, and how the sugar modification is orchestrated with Q formation and insertion, is unknown. Here, we report a total synthesis of the hypermodified nucleoside galactosyl‐queuosine (galQ). The availability of the compound enabled us to study the absolute levels of the Q‐family nucleosides in six different organs of newborn and adult mice, and also in human cytosolic tRNA. Our synthesis now paves the way to a more detailed analysis of the biological function of the Q‐nucleoside family.     

Ultrasonic investigation of the phase transition in flux-grown SrTiO3

Ultrasonic attenuation and velocity have been measured close to and above the 105 K transition in flux-grown SrTiO₃. The data are compared with data from Verneuil-grown SrTiO₃. Larger exponents than expected are observed. The difference between relaxation times in the two samples is interpreted as being due to different impurity contents.     

The concept of special inner products for deriving new conjugate gradient-like solvers for non-symmetric sparse linear systems

Yserentant's and Bramble/Pasciak/Xu's hierarchical preconditioners only require the hierarchical node connection of a finite element grid. So they could be applied to nonsymmetric FE-systems too, having a symmetric preconditioner. We investigate the question whether this fact could be useful in the CG-like iterative methods. The main key is the consideration of an appropriate choice of the inner product defined in the N-vector space. It is shown, how the inner product influences the formulas of the methods, the rate of convergence and some other properties.     

Basin boundaries and bifurcations near convective instabilities: a case study

Using a scalar advection-reaction-diffusion equation with a cubic nonlinearity as a simple model problem, we investigate the effect of domain size on stability and bifurcations of steady states. We focus on two parameter regimes, namely, the regions where the steady state is convectively or absolutely unstable. In the convective-instability regime, the trivial stationary solution is asymptotically stable on any bounded domain but unstable on the real line. To measure the degree to which the trivial solution is stable, we estimate the distance of the trivial solution to the boundary of its basin of attraction: We show that this distance is exponentially small in the diameter of the domain for subcritical nonlinearities, while it is bounded away from zero uniformly in the domain size for supercritical nonlinearities. Lastly, at the onset of the absolute instability where the trivial steady state destabilizes on large bounded domains, we discuss bifurcations and amplitude scalings.     

Ergebnisse von Ballonmessungen an sekundären Elektronen und Photonen

A scintillation counter telescope has been flown in the upper atmosphere at2.4g/cm² from Bergen/Lüneburger Heide for the measurement of electrons and photons of the secondary cosmic radiation. The aim was to get the differential energy spectra of secondary photons in an energy range from 1 to 44 MeV and of secondary and return albedo electrons from 2 to 35 MeV for three different zenith angles (0 °, 90 ° and 180 °). The received photon spectrum is in good agreement to the results of other authors as well to lower as to higher energies. It has been shown, that the spectrum has a great anisotropy with a maximum of intensity around the horizon. The main reason therefore is the atmospheric deepness in the different directions. In this energy range we have found that the Bremsstrahlung of the return albedo electrons is the main reason for the photon flux and secondly the π⁰-decay. The measured electron spectra don't show any significant difference relative to the three zenith angles. These secondary electrons are produced isotropically in the upper atmosphere and they consist of a mixture of secondary and return albedo electrons.