Elementare Eigenschaften lokaler–Polynom–Schätzer: ein Streifzug durch die lineare Algebra

Zusammenfassung. Der lokale–Polynom–Sch?tzer besteht darin, an eine Sequenz von aufeinanderfolgenden Datenpunkten lokal ein Polynom anzupassen und damit zuf?llige Schwankungen in den Daten wegzugl?tten. Dieser Ansatz gewinnt in der nichtparametrischen Kurvensch?tzung st?ndig an Bedeutung. Es wird gezeigt, wie die Herleitung einiger elementarer Eigenschaften dieses Handwerkszeuges des Datenanalytikers einen Streifzug durch die lineare Algebra erforderlich macht. Eingegangen am 27.03.1998 / Angenommen am 15.06.1998     

From the Photosensitizer Hypericin to the Photoreceptor Stentorin- The Chemistry of Phenanthroperylene Quinones

Hypericin and stentorin are the most important representatives of the phenanthroperylene quinones. Their tautomerism, dissociation, conformation, and association equilibria make them structurally complex, and they are interesting on the one hand for medical applications (for example, photodynamic therapy) and on the other as biological photoreceptors.     

Beiträge zur Chemie der Pyrrolpigmente, 39. Mitt.: Ein Kraftfeldmodell zur konformationsanalytischen Untersuchung von Gallenfarbstoffen

A force field model was designed with respect to the special needs of bile pigments. It is parametrized and tested using partial structures of bile pigments as well as an integral pigment; the solution structures of the molecules were previously deduced using independent experimental methods.

38. Mitt::Falk, H., Schlederer, T., Wolshann, P., Mh. Chem.112, 199 (1981).     

Strain localization and percolation of stable structure in amorphous solids

Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the most rapidly quenched samples higher strain rates lead to increased localization, while the more gradually quenched samples exhibit the opposite strain rate dependence. This transition coincides with the k-core percolation of atoms with quasi-crystal-like short range order. The authors infer the existence of a related microstructural length scale.     

Asymptotic conditional distribution of exceedance counts: fragility index with different margins

We consider a random vector X, whose components are neither necessarily independent nor identically distributed. The fragility index (FI), if it exists, is defined as the limit of the expected number of exceedances among the components of X above a high threshold, given that there is at least one exceedance. It measures the asymptotic stability of the system of components. The system is called stable if the FI is one and fragile otherwise. In this paper, we show that the asymptotic conditional distribution of exceedance counts exists, if the copula of X is in the domain of attraction of a multivariate extreme value distribution, and if the marginal distribution functions satisfy an appropriate tail condition. This enables the computation of the FI corresponding to X and of the extended FI as well as of the asymptotic distribution of the exceedance cluster length also in that case, where the components of X are not identically distributed.     

Zur photochemischen (Z)⇆(E)-Isomerisierung von Gallenpigment-Partialstrukturen

The photochemical (Z)?(E) isomerization of the exocyclic double bond is only possible in pyrromethenones (partial structure1) but not in2–4. From spectral investigations, chelation and methylation of certain positions within these structures it can be shown that it is most probably a proton transfer reaction which competes successfully with the isomerization.