This habilitation thesis is concerned with the behaviour of meromorphic functions in the plane in the neighbourhood of infinity. We say that two functions share limit values, if both functions converge to certain given values on the same sequences to infinity. Shared limit values lead to shared islands in a suitable sense, which makes it possible to apply Ahlfors's theory of covering surfaces. For example, we proof a (weak)analogue of Nevanlinna's theorem on five shared values. In the second chapter deficient rational functions and zeros of composite meromorphic functions are studied.

The swelling behaviour of water sensible, chemically crosslinked polyurethanes has been examined in water and mesogenic solvents. The experimental swelling curves have been described with generally known network theories . The swelling curve in a polymer solution has been determined for the first time dependent on temperature. Additionally temperature dependent membrane-osmosis experiments on the system polyethyleneoxide/water have been performed.

According to the TIMS-Study students in Germany show great deficits in problem solving abilities according to a lack of flexibility in thinking in mathematical networks. However, there exists hardly information about the exact lacks and the reasons of the deficits. The aim of the study in this dissertation thesis was to investigate how a mathematical network as it is presented in textbooks is transformed when carried over into students' minds during teaching and learning processes. The thesis subdivides into a theoretical part and the presentation of the empirical investigation. The theoretical part gives first an overview on the didactical discussion to the topic of connections in mathematics education. It follows a conceptual foundation of mathematical networks and their different aspects, pointing out that the underlying structure of a network is a graph, whose vertices represent mathematical objects and nonmathematical components related to these, and whose edges represent existing relations on them. According to the different sorts of relations, network categories with relevance for mathematics education in school are defined. Further, some theories and models describing aspects of genesis, memorizing and recalling connections are presented and information with regard to the different network categories defined above are brought out. The model of curricular frames is discussed as an approach to specify connections in teaching and learning processes; it serves, together with the modelling of connections as graphs, as aids for the empirical investigation. The empirical study particularly focuses on the topic "sets of two equations in straight form" in middle grade classes and restricts on the investigation of some network relations according to subject systematics and a special relation according to the application of mathematical objects, the model relation. The main research questions are: 1. Which relations according to subject systematics and which model relations to the topic focused on are part of curricular frames? 2. Which network transformations result in teaching and learning processes, on the way from the frame of the intended curriculum into the frame of the implemented curriculum and further in the frame of the achieved curriculum? The results show that connections as they are presented in text books are nearly unchanged translated into the frame of the implemented curriculum: teachers follow almost exactly the textbook in their lessons. On the further transfer of the implemented network into students' minds many connections are filtered out: the mainly learned connections by students are part of the links according to subject systematics (links between problems and solving algorithms, linkages according to a subconcept-superconcept relation), model links are hardly known. Students show great difficulties, when they have to use connections in problem solving processes. The study reveals the incompleteness of the transfer of implemented networks into students' minds. Moreover, the missing relations in the achieved networks are pointed out. The results of the study provide useful information for a possible improvement of teaching and learning processes with respect to the different sorts of connections.

The use and function of graphic organizers when reading expository texts was examined. In two experiments the text structure, the design of the diagram and the reading strategy instruction was systematically varied. 120 participants read an expository text on a computer, and process measures (reading time, navigation) as well as product measures (recall, sentence verification) were recorded. The findings show that graphic organizers foster comprehension when the text is well-structured and when the readers use the diagram to review main topics of the text. In this case the dynamic filtering of relevant topics in the diagram (so called Fisheye Views) also have a positive effect. The results are applicable to text- and graphic design in both electronic and print media, and to reading strategy instruction - specifically for the use of graphic organizers in texts.

We consider Lorentz manifolds which carry a conformal gradient field with at least one zero. All such manifolds are necessarily locally conformally flat. If in addition the manifold is developable and the image of a development map is great enough one can describe the global conformal type by a 3-regular graph provided with two additional datas. We get this conformal invariants using certain conformal development maps into the projective standard quadric. All conformal diffeomorphisms of this projective quadric are nothing else than the projectivities of the ambient real projective space which preserve the quadric. In the proofs we often use this fact. As a by-product of a general existence theorem we give an infinite number of locally conformally flat Lorentz metrics on the differentiable manifold R^n which are in pairs not conformally equivalent.

The subject of this thesis is the development and the characterization of threedimensional electrode arrays for the electrostimulation of neural cells. For the development of the electrode fabrication process special attention was paid to the compatibility with existing CMOS processes. This allows the fabrication of electrodes and electronic control circuitry on the same substrate in a close distance without the need of further assembly techniques. The fabrication process of the electrode arrays essentially consists of electrodeposition of gold to form the threedimensional electrode structures and a further electrodeposition of iridium in order to improve the electrode characteristics significantly. Cylic voltammetry and impedance measurements were performed to characterize and compare the fabricated iridium electrode arrays with other common electrode materials such as platinum, gold and titanium nitride. It was shown that the iridium electrodes have lower impedances over the considered frequency ranges and higher permissible clamp voltages for electrostimulation. Furthermore a method and a device for scanning potential microscopy was developed. Measurements of the local potential distribution of different electrode configurations and electrode shapes in saline solutions have been performed using this scanning potential microscope. In this way results obtained by finite element simulations have been verified experimentally. It was also shown that the presented method offers a better spatial resolution than previously reported methods.

This work is subdivided in three chapters. In the first chapter the synthesis of a 7,7'-bridged 1,1'-Biisoquinoline by a Pomeranz-Fritsch-Reaction is described. This molecule was seperated in its atropisomers which racemice in solution. The influence of the solvent character to the rate of racemization was investigated. It has been shown that the more polar and the more protic the solvent is the higher is the rate of racemization. The second chapter introduces an easy synthetic route to 6-substituted Benzimidazo[2,1-a]isoquinolines and in the single case of a Furyl-substituent to Isoindolo[2,1-a]quinoxalins. The starting materials, ortho-Alkynyl-substituted Benzaldehydes, are prepared by Sonogashira-Coupling of the Bromobenzaldehydes with different substituted terminal Alkynes. The reaction of o,o'- Bis(phenylethinyl)-substituted Benzil with Hydroxylamine Hydrochloride leads to a rearranged Benzofluorenon. The formation is explained by a domino process including a cyclization-step, a Hetero-Diels-Alder reaction and the final rearrangement. In the third chapter the stereochemical outcome of the McMurry reaction is investigated depending on the length of a tether between the meta and meta'-position of an Bisbenzaldehyde. Only the short dioxapentandiyl tethered Bisbenzaldehyde forms streoselectiv the cis-product. Starting with the dioxaoctandiyl- or dioxatetradecandiyl-tethered Bisbenzaldehydes the thermodynamical more stable trans products are obtained. In a second part the regioselectivity of the oxidative photocyclization of these McMurry-products, leading to tethered Phenathrenes, has been investigated. The dioxapentandiyl- and the dioxaoctandiyl-substituted Stilbenes leads regioselectiv to the 4,5-disubstituted Phenathrenes. Whereas the longer dioxatetradecandiyl-tether allows a change in the product ratio and the 2,5-disubstituted Phenanthrene is obtained as the major product. In all cases no 2,7-Phenanthrene could be detected.

In the theoretical part of this dissertation theintroduction of the thermodynamics of mixtures is followed by the basicknowledge of lightscattering. The correlation between thermodynamics atthe one hand and lightscattering at the other is demonstrated. In the apparativeand practicel part the development, build and handeling of the high pressurecell and the carrying out of the light scattering experiments are shown.In the part "results and discussion" the interesting and partly surprisingresults are presentet and discussed.

Today the development of industrial CMOS processes with respect to minimum structure size allows the realisation of CMOS image sensors with a spatial resolution comparable to CCD image sensors. While CCD's still provide images of higher quality, CMOS sensors can take advantage of the possibility of monolithic integration of optical sensor devices with analog and digital signal processing as well as high flexibility with respect to sensor readout. CMOS technology allows the realisation of low-cost single-chip camera electronics with very low power consumption and application specific properties. As a basis for future developments of CMOS imaging systems frequently used concepts for optical sensor devices and sensor readout circuits are analysed with respect to noise, dynamic range, linearity and speed. It is shown, how to optimise sensor circuits with respect to these properties. To demonstrate the advantages of CMOS technology compared with CCD technology, two integrated image sensors are presented. The image rs provide a very high input dynamic range and perform on-chip image processing inspired by the funcionality of the human retina.

In this work the generation of shock-waves and short electrical pulses on nonlinear transmission lines (NLTL) showing transients down to 3.6 ps and amplitudes of 1V - are presented. Special emphasis is layed upon the development of monolithic integration of planar schottky-diodes and coplanar waveguide structures based on InP-semiconductor material. The methods of simulating nonliear propagation effects on NLTL, designing and technology of NLTL and at last the experimental investigations in order to measure the generatred transients both in the time domain and frequency domain are shown in detail.