Der Großteil der Erdkruste besteht aus Metalloxiden, wobei Siliziumdioxid, Aluminiumoxid und Eisenoxide die Hauptbestandteile sind. Waren Metalloxide in der Menschheitsgeschichte zunächst hauptsächlich als Pigmente und als Rohstoffe zur Metallgewinnung interessant, so wuchs ihre Bedeutung mit wachsendem chemischem Wissen. Die Mechanismen der Bildung und des Zerfalls von Metalloxiden sind sehr komplex und bisher kaum verstanden. Genau dieses Wissen wird aber benötigt, um Metalloxide mit bestimmten Eigenschaften herzustellen und nutzen zu können. In dieser Arbeit werden daher einfache Silanole als molekulare Modelle für Silikate als Ligandvorläufer verwendet, um Eisensilanolatkomplexe zu synthetisieren. Die daraus erhaltenen Eisensilanolatkomplexe können als strukturelle Modelle für natürliche und synthetische Eisensilikate angesehen werden. Zur Aufklärung der Bildung von Eisensilikaten sowie der Struktur des aktiven Zentrums von eisenhaltigen Zeolithen werden diese Eisensilikate sowohl strukturell als auch spektroskopisch eingehend untersucht und mit den Ergebnissen von natürlichen und synthetischen Eisensilikaten verglichen. Die außergewöhnliche Kombination aus quadratisch planarer Koordination und high-spin Konfiguration der Eisen(II)ionen der in dieser Arbeit diskutierten entstehenden Komplexe entpuppt sich als charakteristisch für das aktive Zentrum von eisenhaltigen Zeolithen, weshalb die Eisensilanolatkomplexe in dieser Arbeit als gute strukturelle Modelle solcher angesehen werden können. / The main part of the earth’s crust consists of metal oxides with silica, alumina and iron oxide as major constituents. Metal oxides were used as pigments and as raw material for metal production, but with increasing chemical knowledge their importance grew. The mechanism of formation and decomposition is complex and still rarely understood. But this knowledge is needed, to synthesize and use metal oxides with distinct properties. In this work simple silanols as molecular models for silicates are used as ligand precursors to synthesize iron silanolate complexes. Those complexes can be considered as structural models for natural and synthetic iron silicates. To understand the mechanism of formation of iron silicates and also the structure of the active centre of iron containing zeolites, those iron complexes are analysed structurally and spectroscopically. The results are compared to those of natural and synthetic iron silicates. The extraordinary combination of square planar coordination and high-spin configuration of the iron(II) ion in the discussed iron complexes turns out to be characteristic for the active centre of iron containing zeolites, thus making the resulting complexes good structural models for the active centre of iron containing zeolites.

Ill-posed inverse problems with quadratic structure are introduced, studied and solved. As an example an inverse problem appearing in laser optics is solved numerically based on a new regularized inversion algorithm. In addition, the theory of sparsity promoting regularization is extended to situations in which sparsity cannot be expected and also to equations with non-injective operators.

Ill-posed inverse problems with quadratic structure are introduced, studied and solved. As an example an inverse problem appearing in laser optics is solved numerically based on a new regularized inversion algorithm. In addition, the theory of sparsity promoting regularization is extended to situations in which sparsity cannot be expected and also to equations with non-injective operators.

Very recently, the tableau-based algorithm for deciding consistency of general fuzzy DL ontologies over the product t-norm was shown to be incorrect, due to a very weak blocking condition. In this report we take the first steps towards a correct algorithm by modifying the blocking condition, such that the (finite) structure obtained through the algorithm uniquely describes an infinite system of quadratic constraints. We show that this procedure terminates, and is sound and complete in the sense that the input is consistent iff the corresponding infinite system of constraints is satisfiable.