On theL p-bounds for maximal functions associated to convex bodies inR n

The dimension-freeL ²-maximal inequality for convex symmetric bodies obtained in [2] is extended forp>3/2.     

Karhunen–Loeve representations of turbulent channel flows using the method of snapshots

For three‐dimensional flows with one inhomogeneous spatial coordinate and two periodic directions, the Karhunen–Loeve procedure is typically formulated as a spatial eigenvalue problem. This is normally referred to as the direct method (DM). Here we derive an equivalent formulation in which the eigenvalue problem is formulated in the temporal coordinate. It is shown that this so‐called method of snapshots (MOS) has some numerical advantages when compared to the DM. In particular, the MOS can be formulated purely as a matrix composed of scalars, thus avoiding the need to construct a matrix of matrices as in the DM. In addition, the MOS avoids the need for so‐called weight functions, which emerge in the DM as a result of the non‐uniform grid typically employed in the inhomogeneous direction. The avoidance of such weight functions, which may exhibit singular behaviour, guarantees satisfaction of the boundary conditions. The MOS is applied to data sets recently obtained from the direct simulation of turbulence in a channel in which viscoelasticity is imparted to the fluid using a Giesekus model. The analysis reveals a steep drop in the dimensionality of the turbulence as viscoelasticity is increased. This is consistent with the results that have been obtained with other viscoelastic models, thus revealing an essential generic feature of polymer‐induced drag reduced turbulent flows. Published in 2006 by John Wiley & Sons, Ltd.     

Secondary ion emission from binary Fe-Cr,Fe-Ni,Cr-Ni and ternary Fe-Cr-Ni alloys: Chemical and physical matrix effects

Secondary ion emission from Fe-Cr, Fe-Ni, Cr-Ni binary alloys and Fe-Cr-Ni ternary alloys (concentration range 10–90% of the alloying element) bombarded with 3 keV Xe⁺ ions has been investigated as a function of concentration of the studied element in the multicomponent system. The linear increase of the secondary ion intensity with concentration of the element in the sample was found only for a low-concentration region. There are pronounced nonlinearities in the medium and high-concentration regions. A possible explanation for such nonlinearities based on chemical and physical matrix effects is proposed.     

Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

Wavelets and adaptive grids for the discontinuous Galerkin method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.     

Ionization potentials and geometrical structure of pure and oxygenated barium clusters

In this article, we present results obtained on structures of small bare and oxygenated barium clusters produced by the laser vaporization technique. Contrary to the very weak Ba—Ba binding (0.202 eV), the Ba—O binding is rather strong (5.8 eV). As a consequence, extremely small amounts of oxygen in the cluster source are sufficient to induce the nucleation of oxygenated barium clusters. Surprisingly, at least for substoechiometric systems, Ba_nO_m clusters exhibit the same icosahedral structure as bare clusters do. Mass spectra seem to indicate that replacing a barium atom with a strongly polar BaO molecule does not affect the geometrical structure of the cluster. This aspect is more easily understandable if we assume that the oxygen atom takes place inside the structure of the Ba_n cluster without significant distortions. Ab-initio calculations have been undertaken in order to give a satisfactory account of this hypothesis.     

Aspects of operator theory in hereditarily indecomposable Banach spaces

We examine certain special features exhibited by various classes of linear operators acting in a hereditarily indecomposable Banach space. For instance, we show that the family of all Riesz operators in a H.I. space forms a closed, 2-sided ideal. We also give further characterizations of the class of scalar-type spectral operators (to those already given in [16]). The final section discusses some properties of the spectral maximal spaces of (necessarily decomposable) linear operators in such spaces. Conferenza tenuta il 16 settembre 1997 The support of the German Academic Exchange Scheme (DAAD) is gratefully acknowledged