Essentially optimal explicit Runge–Kutta methods with application to hyperbolic–parabolic equations

Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL condition even in the presence of viscous fluxes.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Sandwich Techniques in flow injection analysis : Part 1. Continuous recalibration techniques for process control

Flow injection methodology based on sample insertion between two different standard solutions used as carrier streams is described. This approach provides a simple system for continuous recalibration in process control; spectrophotometric and ion-selective electrode procedures are outlined.     

Automatic detection and identification of shocks in Gaussian state‐space models: a Bayesian approach

An automatic monitoring and intervention algorithm that permits the supervision of very general aspects in an univariate linear Gaussian state–space model is proposed. The algorithm makes use of a model comparison and selection approach within a Bayesian framework. In addition, this algorithm incorporates the possibility of eliminating earlier interventions when subsequent evidence against them comes to light. Finally, the procedure is illustrated with two empirical examples taken from the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

151Eu Mössbauer studies on Eu1+x Ba2−x Cu3O7+δ oxide systems

Mössbauer parameters of¹⁵¹Eu in Eu_1+x Ba_2?x Cu₃O_7+δ have been studied as a function of temperature, forx=0.15 andx=0.25. The areas of the absorption spectra for the two samples are almost equal. This could mean that thef-Mössbauer factor for¹⁵¹Eu at the barium sites is much smaller than that for¹⁵¹Eu at the rare earth sites, i.e. we only observe the spectra of the latter sites. According to this, the fits of the spectra with a single quadrupolar pattern and with two quadrupolar patterns have given equivalent χ² values.     

Biomagnetic measurements utilising a superparamagnetic marker: a feasibility study

Summary A preliminary study is here reported on a new potential marker for biomagnetic measurements. The marker consists of superparamagnetic polymer microspheres which were detected in the presence of external steady magnetic fields by means of an r.f.-SQUID magnetometer. The particles were prepared in samples differing in the concentration value and immersed in a homogeneous magnetic field of variable intensity. A simple model was taken into account for the distribution of the microspheres in the samples, so that the theoretical values were compared to the marker field values measured by the biomagnetic sensor. The overall sensitivity of the experimental apparatus and the minimum concentration value of the marker were then estimated.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.     

Charge-changing cross sections of the neutron-rich isotopes8,9,11Li

Total charge-changing cross sections have been measured for⁸Li on C and Pb targets, for⁹Li on C, Al, Cu, Sn and Pb targets, as well as for¹¹Li on C, Sn and Pb targets at about 80 MeV/nucleon. These data are compared to measured total reaction cross sections and Glauber-type calculations using Hartree-Fock density distributions. These comparisons allow to draw conclusions on the proton density distribution of the neutronrich lithium isotopes. The results show that even for the most exotic nucleus¹¹Li the proton distribution is only very weakly influenced by the long tail in the neutron density distribution already established in several experiments.