Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

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).     

Filter-radiometer-based realization of candela and establishment of photometric scale at UME

The luminous intensity unit of candela was realized based on filter-radiometer, which is traceable to detector-based primary standard electrical substitution cryogenic radiometer (ESCR). In that realization the traditional Osram Wi41/G-type incandescent lamp and filter-radiometer consisting of an aperture, a V(λ) filter and a silicon photodiode based trap detector were used as light source and detection element, respectively. Measurement techniques of effective aperture area, spectral transmittance of V(λ) filter and absolute responsivity of trap detector are also presented.     

Recombination of Au25+ with free electrons at low energies

The origin of the widely observed enhancement of rates for electron-ion recombination at very low energies is still unknown. We investigated the recombination of Au²⁵⁺ with free electrons in a merged-beams experiment at the UNILAC accelerator of the GSI in Darmstadt. At E _rel= 0 eV we found an enormous enhancement factor of 365 compared to the theory of radiative recombination. An increase of the electron density by a factor of 10 had not much influence on the measured rate coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Witt ring of a Brauer–Severi variety

For a Brauer–Severi variety X over a field k of characteristic not two, every symmetric bilinear space over X up to Witt equivalence is defined over k. Received: 2 February 1998     

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

Anisotropic transport of charge and complexified duality

Charge transport in two dimensions provides an ideal laboratory for investigating parameter space geometries. The Onsager relations for anisotropic transport in a parity-violating external field endow these spaces with a highly nontrivial complex (and Kähler) structure, which can be given a simple geometrical interpretation. A large class of Coulomb gases exhibiting this structure have a generalized Kramers-Wannier symmetry (complexfield duality) which is contained in the modular group. Knowledge of this symmetry and the degrees of freedom encoded in the Coulomb gas appear to be sufficient to determine the global phase diagram and the renormalization group fixed-point structure, including the critical exponents. This accounts for all the scaling behavior observed so far in the quantum Hall system.     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.