Addendum to “A definable nonstandard enlargement”

?o?'s theorem for bounded D ‐ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [4], is established. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffraction of light by supersonic waves: The solution of the raman-nath equations

The partial differential equation associated with the system of difference-differential equations of Raman-Nath for the amplitudes of the diffracted light-waves is solved exactly by the method of the separation of the variables. The solution is presented as a double infinite series containing the Fourier coefficients of the even periodic Mathieu functions with periodπ and the corresponding eigenvalues. Considering this solution as a Laurent series in one of the variables, the Laurent coefficients immediately give the exact expressions for the amplitudes of the diffracted light-waves, from which the formulae for the intensities are calculated. The connection between the Raman-Nath method and Brillouin’s Mathieu function method has thus been achieved.     

Ordinal patterns in epileptic brains: Analysis of intracranial EEG and simultaneous EEG-fMRI

Epileptic seizures are associated with high behavioral stereotypy of the patients. In the EEG of epilepsy patients characteristic signal patterns can be found during and between seizures. Here we use ordinal patterns to analyze EEGs of epilepsy patients and quantify the degree of signal determinism. Besides relative signal redundancy and the fraction of forbidden patterns we introduce the fraction of under-represented patterns as a new measure. Using the logistic map, parameter scans are performed to explore the sensitivity of the measures to signal determinism. Thereafter, application is made to two types of EEGs recorded in two epilepsy patients. Intracranial EEG shows pronounced determinism peaks during seizures. Finally, we demonstrate that ordinal patterns may be useful for improving analysis of non-invasive simultaneous EEG-fMRI.     

Janus micelles induced by olefin metathesis

A facile one-step procedure for hydrophobic modification and simultaneous TEM contrast enhancement via a regioselective olefin metathesis reaction using Grubbs' catalyst is presented. Polyether diblock copolymers were investigated, and both the chain ends of the hydrophilic and the hydrophobic block were hydrophobically modified. Modification of the hydrophilic block results in nonsymmetric supramolecular structures (Janus micelles) which self-assemble into larger hierarchically organized super-micelles.     

Electron tomography shows molecular anchoring within a layer-by-layer film

The layer-by-layer self-assembly of thin films consisting of alternating layers of DNA and bis-urea nanoribbons prevents diffusion of the components within the film and allows the anchoring of biotinylated molecules through molecular recognition in a predetermined layer of the film. Electron tomography demonstrates with nanometer precision the location of gold-labeled streptavidin bound to the incorporated biotinylated molecules.