Bounding the Clique‐Width of H‐Free Chordal Graphs

A graph is H‐free if it has no induced subgraph isomorphic to H. Brandstädt, Engelfriet, Le, and Lozin proved that the class of chordal graphs with independence number at most 3 has unbounded clique‐width. Brandstädt, Le, and Mosca erroneously claimed that the gem and co‐gem are the only two 1‐vertex P₄‐extensions H for which the class of H‐free chordal graphs has bounded clique‐width. In fact we prove that bull‐free chordal and co‐chair‐free chordal graphs have clique‐width at most 3 and 4, respectively. In particular, we find four new classes of H‐free chordal graphs of bounded clique‐width. Our main result, obtained by combining new and known results, provides a classification of all but two stubborn cases, that is, with two potential exceptions we determine all graphs H for which the class of H‐free chordal graphs has bounded clique‐width. We illustrate the usefulness of this classification for classifying other types of graph classes by proving that the class of ‐free graphs has bounded clique‐width via a reduction to K₄‐free chordal graphs. Finally, we give a complete classification of the (un)boundedness of clique‐width of H‐free weakly chordal graphs.     

Thin liquid droplet on top of a rotating non-isothermal liquid layer

Wafers are usually coated by using spin-coating, where centrifugal forces are used to spread a droplet on the rotating wafer. This flow is unstable to the fingering instability, where several segments of the wetting front spread faster than the average, resulting in several fingers. The liquid flows via the existing fingers while the area in between does not get coated. A precise experimental investigation is problematic, as the droplet has to be placed quite exactly in the center of the rotation. Replacing the wafer by a second liquid should lead to a parabolic-shaped free interface and the droplet should center itself due to gravity. Here, we derive a model for the free interfaces of a thin droplet on top of a rotating liquid by taking gravity, centrifugal forces, friction, (thermo-)capillary and line forces into account. Additionally, this setup is the simplest example of multiple coating, where several free interfaces and contact lines influence each other. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stratified Monte Carlo Quadrature for Continuous Random Fields

We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behaviour is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the Hölder class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.     

Investigation of structural changes in semi-crystalline polymers during deformation by synchrotron X-ray scattering

The mechanical behavior of polymer materials is strongly dependent on polymer structure and morphology of the material. The latter is determined mainly by processing and thermal history. Temperature-dependent on-line X-ray scattering during deformation enables the investigation of deformation processes, fatigue and failure of polymers. As an example, investigations on polypropylene are presented. By on-line X-ray scattering with synchrotron radiation, a time resolution in the order of seconds and a spatial resolution in the order of microns can be achieved. The characterization of the crystalline and amorphous phases as well as the study of cavitation processes were performed by simultaneous SAXS and WAXS. The results of scattering experiments are complemented by DSC measurements and SEM investigations. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1574–1586, 2010     

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Über einen Hauptsatz in der Theorie der konvexen Polyeder

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Bemerkung über das parabolische Strahlennetz und das zugehörige Zylindroid

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Dihydrazidophosphoric Acid Derivatives as Starting Materials for Inorganic Heterocycles with Unusual Ring Conformations

Abstract

Reported are synthetic routes to inorganic heterocycles of different ring size, containing phosphorus, hydrazine, silicon and other elements as ring components. Steric effects that cause saturated sixmembered rings to adopt an unusual twist conformation are discussed (temperature dependent NMR-spectra, X-ray structures).