Die vorliegende Arbeit befasst sich mit dem Versuch der Optimierung von Simulated Annealing. Genauer gesagt, werden Simulationsergebnisse für einfache Spinglassysteme in Abhängigkeit von verschiedenen Nachbarschaftsmodellen berechnet – jeweils unter Verwendung des optimalen Abkühlverlaufs. Ziel ist es, eine Faustregel für die dynamische Anpassung der Nachbarschaftsbeziehung während einer Annealing-Simulation zu finden. / The thesis at hand presents an attempt to optimize simulated annealing. In particular, annealing results are computed based on different move class definitions for Ising spin systems while simultaneously applying an existing algorithm to determine the optimal temperature schedule for each case. The aim is to find a rule of thumb for dynamic adjustment of the move class during an annealing run.

This text is concerned with the Fredholm theory and stable approximation of bounded linear operators generated by a class of infinite matrices $(a_{ij})$ that are either banded or have certain decay properties as one goes away from the main diagonal. The operators are studied on $\ell^p$ spaces of functions $\Z^N\to X$, where $p\in[1,\infty]$, $N\in\N$ and $X$ is a complex Banach space. The latter means that our matrix entries $a_{ij}$ are indexed by multiindices $i,j\in\Z^N$ and that every $a_{ij}$ is itself a bounded linear operator on $X$. Our main focus lies on the case $p=\infty$, where new results are derived, and it is demonstrated in both general theory and concrete operator equations from mathematical physics how advantage can be taken of these new $p=\infty$ results in the general case $p\in[1,\infty]$.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

Die Broschüre bildet den fachlichen Standard bei der Ausweisung von Trinkwasserschutzgebieten für sächsische Sickerleitungsquellen und deren Speisungsgebiete ab. Sie gibt Hilfestellung bei der Erarbeitung von Fachgutachten und ist an Wasserbehörden, Wasserversorgungsträger, Ingenieurbüros und an die interessierte Öffentlichkeit gerichtet. Als Methodensammlung und als Leitfaden zur Erstellung und Bewertung von Fachgutachten unterstützt sie die Ausweisung von rechtssicheren Trinkwasserschutzgebieten für Sickerleitungsquellen.

Das Einzugsgebiet der Mulde mit Zwickauer, Freiberger und Vereinigter Mulde ist allein in den letzten 15 Jahren von mehreren extremen Hochwassern heimgesucht worden. In der vorliegenden Studie wurden die größten Hochwasser im Muldegebiet seit 1950 unter hydrologischen und meteorologischen Gesichtspunkten verglichen. Auf Grundlage der vorhandenen Gemeinsamkeiten und Unterschiede bei der Hochwasserentstehung und dem Hochwasserverlauf wurden neue Informationen über den räumlich differenzierten Ablauf derartiger Extremereignisse gewonnen.

Das Werk ist eine Chronologie der mathematisch-naturwissenschaftlichen Entdeckungen und deren Protagonisten. Es enthält ca. zwölftausend Einträge über Entdeckungen und Erfindungen mit den Namen jener Personen, die in den einzelnen Disziplinen (Mathematik, Physik, Chemie, Astro-, Geo- und Biowissenschaften) Entdeckungen gemacht haben. Das Nachschlagewerk ist nach Jahren geordnet und umfasst den Zeitraum zwischen 10.000 v.Chr. bis 1990. Das Werk ergibt damit ein Bild von dem langen und komplizierten Prozess, der von den ersten Erfahrungen und Erkenntnissen über die Natur zu einzelnen wissenschaftlichen Kenntnissen über deren Teilgebiete, dann zu systematischem Wissen über diese Teilgebiete und schließlich zu den heutigen Naturwissenschaften führte. Für die Vor- und Frühgeschichte sind dabei auch Leistungen berücksichtigt, denen das Attribut der Wissenschaftlichkeit zwar nur bedingt zuerkannt werden kann, deren Aufnahme jedoch unabdingbar ist, um die historischen Entwicklungslinien im vollen Umfang nachzuzeichnen. Die Geowissenschaften sind in ihrer ganzen, auch die Länder- bzw. Völkerkunde umfassenden Breite vertreten, wobei auch die Anfänge jener Entwicklungen berücksichtigt wurden, die später zu den heute oft als Humangeographie bezeichneten sozial- und geisteswissenschaftlichen Komponenten der Geowissenschaften (Sozial-, Verkehrs-, Wirtschaftsgeographie usw.) führten. Zudem enthält das Werk Daten zu frühen Universitätsgründungen, zur Formierung verschiedener philosophischer Ideen und Systeme, zur Entstehung bedeutender Akademien, zur Gründung von Vereinigungen der einzelnen Disziplinen, zur Herausgabe von Zeitschriften und zur Konstruktion von wissenschaftlichen Geräten, die – wie Mikroskop, Fernrohr oder Teilchenbeschleuniger – die weitere Forschung maßgeblich beeinflussten. Eine besondere Rolle spielte die Umsetzung naturwissenschaftlicher Ideen in technologischen Verfahren und die sich dabei ergebenden Rückwirkungen auf den Erkenntnisfortschritt in der jeweiligen Disziplin. Die Fülle der Einträge ermöglicht es, eine Vorstellung von den bestimmenden Entwicklungslinien der einzelnen naturwissenschaftlichen Gebiete und der Mathematik in einem beliebigen Zeitraum zu gewinnen und zu erkennen, welchen Platz sie und ihre Disziplinen in der Entwicklung der menschlichen Gesellschaft eingenommen haben bzw. wie sich diese Rolle im Laufe der Jahrhunderte veränderte. Zugleich werden auch die Wechselwirkungen zwischen den einzelnen Disziplinen deutlich.:Geleitwort Vorwort und Danksagung Benutzerhinweise Autoren und deren Beiträge Epochen Vorgeschichte und frühe Hochkulturen Griechisch-hellenistische Antike Mittelalter Renaissance, Humanismus, Reformation Wissenschaftliche Revolution und Rationalismus Die Zeit des Durchbruchs zur Industriewirtschaft Der Industriekapitalismus am Ende des 19. und im Übergang ins 20. Jahrhundert Die Herausbildung der modernen Naturwissenschaften Die Zeit des kalten Krieges Verzeichnisse Verzeichnis der Nobelpreisträger Literaturverzeichnis Personenverzeichnis Sachwortverzeichnis

Since the discovery of transfer RNAs (tRNAs) as decoders of the genetic code, life science has transformed. Particularly, as soon as the importance of tRNAs in protein synthesis has been established, researchers recognized that the functionality of tRNAs in cellular regulation exceeds beyond this paradigm. A strong impetus for these discoveries came from advances in large-scale RNA sequencing (RNA-seq) and increasingly sophisticated algorithms. Sequencing tRNAs is challenging both experimentally and in terms of the subsequent computational analysis. In RNA-seq data analysis, mapping tRNA reads to a reference genome is an error-prone task. This is in particular true, as chemical modifications introduce systematic reverse transcription errors while at the same time the genomic loci are only approximately identical due to the post-transcriptional maturation of tRNAs. Additionally, their multi-copy nature complicates the precise read assignment to its true genomic origin. In the course of the thesis a computational workflow was established to enable accurate mapping of tRNA reads. The developed method removes most of the mapping artifacts introduced by simpler mapping schemes, as demonstrated by using both simulated and human RNA-seq data. Subsequently, the resulting mapping profiles can be used for reliable identification of specific chemical tRNA modifications with a false discovery rate of only 2%. For that purpose, computational analysis methods were developed that facilitates the sensitive detection and even classification of most tRNA modifications based on their mapping profiles. This comprised both untreated RNA-seq data of various species, as well as treated data of Bacillus subtilis that has been designed to display modifications in a specific read-out in the mapping profile. The discussion focuses on sources of artifacts that complicate the profiling of tRNA modifications and strategies to overcome them. Exemplary studies on the modification pattern of different human tissues and the developmental stages of Dictyostelium discoideum were carried out. These suggested regulatory functions of tRNA modifications in development and during cell differentiation. The main experimental difficulties of tRNA sequencing are caused by extensive, stable secondary structures and the presence of chemical modifications. Current RNA-seq methods do not sample the entire tRNA pool, lose short tRNA fragments, or they lack specificity for tRNAs. Within this thesis, the benchmark and improvement of LOTTE-seq, a method for specific selection of tRNAs for high-throughput sequencing, exhibited that the method solves the experimental challenges and avoids the disadvantages of previous tRNA-seq protocols. Applying the accurate tRNA mapping strategy to LOTTE-seq and other tRNA-specific RNA- seq methods demonstrated that the content of mature tRNAs is highest in LOTTE-seq data, ranging from 90% in Spinacia oleracea to 100% in D. discoideum. Additionally, the thesis addressed the fact that tRNAs are multi-copy genes that undergo concerted evolution which keeps sequences of paralogous genes effectively identical. Therefore, it is impossible to distinguish orthologs from paralogs by sequence similarity alone. Synteny, the maintenance of relative genomic positions, is helpful to disambiguate evolutionary relationships in this situation. During this thesis a workflow was computed for synteny-based orthology identification of tRNA genes. The workflow is based on the use of pre-computed genome-wide multiple sequence alignment blocks as anchors to establish syntenic conservation of sequence intervals. Syntenic clusters of concertedly evolving genes of different tRNA families are then subdivided and processed by cograph editing to recover their duplication histories. A useful outcome of this study is that it highlights the technical problems and difficulties associated with an accurate analysis of the evolution of multi-copy genes. To showcase the method, evolution of tRNAs in primates and fruit flies were reconstructed. In the last decade, a number of reports have described novel aspects of tRNAs in terms of the diversity of their genes. For example, nuclear-encoded mitochondrial-derived tRNAs (nm-tRNAs) have been reported whose presence provokes intriguing questions about their functionality. Within this thesis an annotation strategy was developed that led to the identification of 335 and 43 novel nm-tRNAs in human and mouse, respectively. Interestingly, downstream analyses showed that the localization of several nm-tRNAs in introns and the over-representation of conserved RNA-binding sites of proteins involved in splicing suggest a potential regulatory function of intronic nm-tRNAs in splicing.

In this thesis, we bring forward the study of the spectral properties of graphs and we extend this theory for chemical hypergraphs, a new class of hypergraphs that model chemical reaction networks.

Manufacturing of components with complex internal features, e.g. for medical applications, aeronautics or automobile industry, is challenging. Those components are often machined in temporarily and locally separated production stages. As results of these separated stages form deviations and positioning errors increase, which lead to additional efforts for the quality assurance. The technology aimed within the project SwitchECM is expected to allow the machining of different complex features of one workpiece in one single production stage and shall simultaneously allow a high precision. For this purpose, a multi-cathode system will be developed, in which separated cathodes can be switched with specific parameters, depending on the requirements of the pre-defined features. This study will show the capability to machine the workpiece with different parameter sets but the same cathode and device as fundamental work for the machining with a multi-cathode system. Therefore the surface and dissolution characteristics for the material 1.4301 were used to design the process. The machining tasks were determined to deburring and edge shaping. In the experiments, the parameters voltage and working time were selected depending on the final geometry. It will be shown that the deburring task can be handled with nearly no edge shaping and the edge shaping task is suitable to adjust different edge geometries.