A hyperbolic surface with a square grid net

We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line and such that the preimage of the extended real line under the projection map is homeomorphic to the square grid in the plane. This answers a question raised by è. B. Vinberg. Supported by the Alexander von Humboldt Foundation. Supported by NSF grants DMS-0400636, DMS-0244421, and DMS-0244547.     

Dielectric characterization of samples showing the SmCPA/B7 transition

Dielectric measurements on samples consisting of banana-shaped molecules with a polymorphism I/SmCP_A/B₇ have been performed for the first time. The dielectric increment for the reorientation of the molecules about the long axis, and the corresponding relaxation time, surprisingly decrease at the SmCP_A/B₇ transition. This effect is discussed in terms of the undulated structure which partially destroys the ferroelectric short range order. Decreasing temperature gives an even stronger hindrance for this reorientation and could explain controversial results obtained in the B₇ phases of different samples. At lower temperatures a further mesophase was detected. This was additionally observed by calorimetric and atomic force microscopy methods.     

Anisotropy and temperature dependence of small angle neutron scattering from silicon-oxide precipitates in silicon

Czochralski grown silicon crystals contain interstitially dissolved oxygen which diffuses on heating to form precipitates of silica. We have examined these precipitates by small angle neutron scattering (SANS) in the Q-range 0.05 Å^–1<Q<0.4 Å^–1. The obtained SANS patterns reveal pronounced anisotropic intensity distributions which resemble the symmetry of the host crystal. The SANS spectra show an anisotropic central peak at Q<0.1 Å^–1 due to the single particle shape and a number of weak intensities for larger Q-values. These weak side maxima are considered correlation peaks or quasi-elastic interference peaks. They show, however, an unexpected and distinct temperature dependence: with decreasing temperature below values of 220 K their intensity is lost slowly, but reversibly. At T = 50 K only the central peak from the single-particle scattering remains unchanged. Upon heating, the correlation peaks regain their former value of intensity and Q-position without any evidence of thermal hysteresis.     

Absorption and emission spectroscopy in scattering media: modelling of fluorescence decay curves and photometric laws for systems with inhomogeneous absorber distribution

Summary The optical absorption and fluorescence of scattering samples is investigated theoretically and experimentally under the condition of steady-state and pulsed irradiation, taking into account inhomogeneous distribution of the absorbing species. Based on the Kubelka-Munk model, numerical iterative expressions for the steady-state and time-resolved light flues of excitation and emission are derived. The intensities of reflected, transmitted and forward or backward emitted radiation in layered samples with vertical concentration gradients are discussed. Modification of fluorescence spectra and decay curves due to self absorption, background absorption, secondary emission and time of flight dispersion are calculated and compared to experimental data of hydrocarbons adsorbed on polycrystalline silica gel.     

Photon statistics in saturated m-photon amplification and attenuation of coherent light

The change of photon statistics of a nearly coherent single-mode light beam travelling through a saturable m-photon-amplifying or absorbing medium (m = 1, 2, …) is theoretically investigated. With the help of an approximation scheme valid for $\text{n}$ ? 1, Δn² ? $\text{n}$² ($\text{n}$ mean value and Δn² variance of the photon number) an analytical expression is derived for the quantity Δn²/$\text{n}$. The results holds for arbitrary values of the initial population inversion and of the degree of saturation. It turns out that for both amplification and attenuation processes after sufficiently strong interaction Δn²/$\text{n}$ tends to an asymptotic value.     

Reelle algebraische Funktionen mit vorgegebenen Null- und Polstellen

This note continues the investigations of Knebusch on algebraic curves over real closed fields and was initiated by reading [3]. Especially we ask for the existence of real algebraic functions with given zeroes and poles, a question going back to Witt [4]. We study the real nature of coverings of real algebraic curves, and if the covering has degree two, we get algebraic proofs for results, which in the classical case have been obtained by topological methods in [2].