A quasiconformal dynamic property of the disk

It is known that every conformai embedding of the disk into the extended complex plane possesses a r²-quasiconformal extension across eachr-level line (the r²-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which is not a disk does not admit ther ²-property. Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.     

Intra-cavity spectroscopy with diode lasers

A multi-mode diode laser with an external cavity is studied experimentally and theoretically for its application to intra-cavity spectroscopy. One facet of a typical Ga_0.89Al_0.11As laser diode was antireflection-coated by deposition of HfO₂ such that 10^–3 residual reflectivity was left over. This diode was placed in an external optical cavity. The emission spectrum of this diode laser is highly sensitive to any frequency-dependent loss in the cavity, and the detectivity of such a loss grows with the pump rate. Even close to threshold, the absorption at 780 nm of Rb atoms with a density of 5×10¹⁰ cm^–3 has been detected. An adequate model for diode lasers based on rate equations and including frequency-dependent gain saturation is developed and applied to the calculations of output spectra. The sensitivity of these spectra to intra-cavity absorption is determined by the overall cavity loss — which is rather high — and the fraction of spontaneous emission in the total emission, in contrast with dye lasers where it is limited by nonlinear mode coupling. Various criteria for the sensitivity are suggested. The smallest detectable absorption with a perfectly antireflection-coated laser is 10^–6 cm^–1. Improvement of the characteristics of the laser diode would increase the sensitivity.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

Realisation and metrological characterisation of thickness standards below 100 nm

High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO₂ on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh     

Effective-field theory and the nuclear many-body problem

We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.     

The efficacy of tilted axial MRI of the CNS

The angle between the straight axial plane and the orbito-meatal line was measured in 156 consecutive magnetic resonance examinations. Inconsistent head positioning caused this angle to vary by as much as 44 degrees. Careful positioning of the patient by the technologist can minimize this variability, leading potentially to improved image interpretation. To assess the merit of a standardized orientation for MR examinations of the head, straight axial and tilted axial MR scans were compared in 34 patients. The tilted images were obtained parallel to the orbito-meatal line and were found to be superior for visualization of the cerebellum. When correlative x-ray CTs are available or when an abnormality in the posterior fossa is suspected, tilted axial MR scans should be employed.     

Skew Models II

If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.      

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.