Hugo von Langenstein (Martina 292,36-39) widmete im Jahre 1293 dem Martyrium der Martina (Martina 292,66-71) eine deutschsprachige Heiligenlegende epischen Ausmaßes von einer Märtyrerin vom unzerstörbaren Leben, die heute gemeinhin als die älteste geistliche Dichtung des orden des hospitâles sente Marîen des Dûschen hûses von Jherusalem gelten kann, wenn man von der möglichen Neudatierung Heinrich von Heslers Apokalypse, der Unsicherheit bei der Datierung der Judith und der generellen Skepsis gegenüber der Auffassung eines homogenen Literaturbetriebs innerhalb des Deutschordens absieht. Die passio der Martina hat frömmigkeitsgeschichtlich keine herausragende Wirksamkeit entfaltet - ein Befund, der sich ohne weiteres auch auf die Würdigung in der literatur- und sprachwissenschaftlichen Forschung übertragen ließe. Der Text ist nur in einer einzigen Handschrift aus dem 14. Jahrhundert überliefert. Eine kritische Edition der Legende mit sprachlicher Analyse aus dem Baseler Codex, in dem neben der Martina die Mainauer Naturlehre, beide aus der Hand von Cvnrat von sant Gallen um 1300,8 und der Litauer Schondochs überliefert sind, steht noch aus. In den großen, populären Legendensammlungen des Mittelalters fehlt die heilige Martina. Weder ‚Väterbuch‘ (um 1280), noch ‚Passional‘ (um 1300) erwähnen sie. Auch in der ursprünglichen, lateinischen Fassung der ‚Legenda aurea‘ des italienischen Dominikaners Jacobus de Voragine kommt Martina nicht vor. Unter dem Fokus des Begriffs der „Textallianzen“ darf dem Umstand, dass die passio der Martina gerade im Orden des deutschen Hauses beinahe unbekannt geblieben ist, Aufmerksamkeit geschenkt werden. Wenn man vom derzeitigen Diskussionsstand ausgeht, werden zwei Implikationen des Begriffs „Textallianz“ für unseren Zusammenhang wichtig. Von einer Textallianz kann zum einen dann gesprochen werden, wenn im Rahmen einer Überlieferungsgemeinschaft Exemplare unterschiedlicher Textsorten kompiliert sind. In diesem Sinne wäre der Baseler Codex als „Textallianz“ zu charakterisieren. Zum anderen ist als „Textallianz“ auch die „Bildung einer Textsorte oder einer textsortenähnlichen Klasse durch verschiedene Textindividuen“ aufzufassen, zu der auch Exemplare zugerechnet werden können, die in eine andere Textsorte transformiert werden. Für die Kennzeichnung dieser Phänomene bietet sich dann neben dem Begriff der „Textallianz“ auch der der „Textsortengruppe“ an, der für die Beschreibung der Martina in diesem Sinne verwendet werden wird. Bemerkenswert an der Überlieferungsgeschichte der Martina ist, dass sie, obwohl sie wie das Väterbuch (um 1280) und das Passional (um 1300) „wohl im, oder jedenfalls für den Deutschen Orden entstanden“ ist, im Kontext des Ordens selbst nicht der Textsorte und damit dem Überlieferungszusammenhang der Heiligenlegenden („Textsortengrup- pe“) zugeordnet wird, sondern in einer anderen „Textallianz“ verbleibt, obwohl sie durch intertextuelle Bezüge und Erzählmuster als Heiligenlegende ausgewiesen ist. Aus dieser Perspektive möchte ich hier folgenden Fragen nachgehen: Ist die passio noch der Textsorte Heiligenlegende als Variante zuzurechnen? In welchem Verhältnis steht die Martina zu ‚der‘ Deutschordensliteratur und zum institutionellen und historischen Kontext des Ordens? [Aus der Einleitung]:I. Einleitung II. Forschungspositionen zum Textstatus der Martina III. Div ander marter der Martina III.1. Die zweite Marter aus der Perspektive der kognitiven Semantik und Textlinguistik III.2. Die Marterepisode als Lektion bei Tisch? IV. Martina und der Orden vom Deutschen Haus IV.1. Die passio der Martina und ‚die‘ Deutschordensliteratur

It is known that boron containing compounds exhibit interesting chemical and physical properties. In the past 50 years modern preparative methods have led to an overwhelming number of different structures of novel and often unexpected boron–sulfur and boron–selenium compounds. Among all these new compounds, there was only one which comprises rare earth metal (RE), boron and heavier chalcogen, namely sulfur, the europium thioborate Eu[B2S4] [1]. Selenoborates of rare earth metals are hitherto unknown. On the other hand, rare earth oxoborates represent a well-known class of compounds [2] with a wide range of applications, especially in the field of optical materials. In addition, well-defined boron compounds containing the heavier group 16 elements are fairly difficult to prepare due to the high reactivity of in situ formed boron chalcogenides towards most container materials at elevated temperatures. The chalcogenoborates of the heavier chalcogens are sensitive against oxidation and hydrolysis and therefore have to be handled in an inert environment. Therefore, developing and optimization of preparative routes for the syntheses of pure and crystalline RE thio- and selenoborates was needed. In the course of this study, the application of different preparation routes, such as optimized high-temperature routes (HT), metathesis reactions and high-pressure high-temperature routes (Hp – HT), led to sixteen new rare earth thioborates. Their crystal structures were solved and/or refined from powder and single crystal X-ray diffraction data, while the local structure around rare earth metal was confirmed from the results of the EXAFS analyses. Quantum mechanical calculations were used within this work in order to investigate the arrangement of intrinsic vacancies on the boron sites in the crystal structures of rare earth thioborates. Thermal, magnetic and optical properties of these compounds are also discussed. The rare earth thioborates discovered during this work are the first examples of ternary thioborates containing trivalent cations. These compounds can be divided into two groups of isotypic compounds: the rare earth orthothioborates with general formula REIII[BS3] (RE = La – Nd, Sm, Gd and Tb) [3] and the rare earth thioborate sulfides with general formula REIII¦9B5S21, (RE = Gd – Lu, and Y) [4]. In the crystal structure of RE[BS3] (orthorhombic, space group Pna21, Z = 4), the sulfur atoms form the vertices of corrugated kagome nets, within which every second triangle is occupied by boron and the large hexagons are centered by RE cations. The structural features of the isotypic RE[BS3] phases show great similarities to those of rare earth oxoborates RE[BO3] and orthothioborates of alkali and alkaline earth metals as well as to thallium orthothioborate, yet pronounced differences are also observed: the [BS3]3– groups in the crystal structures of RE[BS3] are more distorted, where the distortion decreases with the decreasing size of the RE element, and the coordination environments of the [BS3]3– groups in the crystal structures of RE[BS3] are different in comparison with the coordination environments of the [BO3]3– groups in the crystal structures of λ-Nd[BO3] [5] and of o-Ce[BO3] [6]. The results of the IR and Raman investigations are in agreement with the presence of [BS3]3– anions in the crystal structure of RE[BS3]. Thermal analyses revealed the thermal stability of these compounds under inert conditions up to ~ 1200 K. Analyses of the magnetic properties of the Sm, Gd and Tb thioborates showed that both Gd and Tb phases order antiferromagnetically. The magnetic susceptibility for Sm orthothioborate approximately follows the Van-Vleck theory for Sm3+. Between 50 K and 62 K a transition appears which is independent of the magnetic field: the magnetic susceptibility becomes lower. This effect might indicate a discontinuous valence transition of Sm which was further investigated by means of XANES and X-ray diffraction using synchrotron radiation, both at low temperatures. The series of isotypic RE thioborate sulfides with composition RE9B5S21, was obtained by the application of Hp – HT conditions to starting mixtures with the initial chemical composition “REB3S6“, after careful optimization of the pressure, temperature and treatment time, as well as the composition of the starting mixtures. Their crystal structures adopt the Ce6Al3.33S14 [7] structure type (hexagonal, space group P63, Z = 2/3). The special features of the RE9B5S21 crystal structures, concerning boron site occupancies and different coordination environments of the two crystallographically independent boron sites, were investigated in more detail by means of quantum chemical calculations, electron diffraction methods, optical and X-ray absorption spectroscopy as well as by 11B NMR spectroscopy. The results obtained from these different experimental and computational methods are in good mutual agreement. The crystal structures of the RE9B5S21 compounds are characterized by two types of anions: tetrahedral [BS4]5– and trigonal planar [BS3]3– as well as [(S2–)3] units. Isolated [BS4]5– tetrahedra (all pointing with one of their apices along the polar [001] direction) represent a unique feature of the crystal structure which is observed for the first time in a thioborate compound. These tetrahedra are stacked along the three-fold rotation axes. Vacancies are located at the trigonal-planar coordinated boron site with preferred ordering –B–B––B–B–– along [001]. No superstructure is observed by means of electron diffraction methods as adjacent columns are shuffled along the c axis, giving rise to a randomly distributed vacancy pattern. Positions of the sulfur atoms within the [(S2–)3] substructure as well as planarity of the [BS3]3– units were investigated in more detail by means of quantum mechanical calculations. Results of the IR and Raman spectroscopy, as well as of the 11B NMR spectroscopy are in agreement with the presence of the boron atoms in two different coordination environments. Thermal analyses showed that compounds RE9B5S21 are stable under inert conditions up to ~ 1200 K. In accordance with the combined results of experimental and computational investigations, the chemical formula of the RE9B5S21 compounds is consistent with RE3[BS3]2[BS4]3S3. A short overview of investigations towards rare earth selenoborates, where in most of the cases only known binary rare earth selenides could be identified, is presented as well in this work. Investigations in the RE–B–Se systems were conducted by the application of different preparation routes by varying the experimental parameters and the initial compositions of the starting mixtures. Although no crystal structure of a ternary phase in these systems could be solved, there are indications that such phases exist, but further investigations are needed. [1] M. Döch, A. Hammerschmidt, B. Krebs, Z. Anorg. Allg. Chem., 2004, 630, 519. [2] H. Huppertz, Chem. Commun., 2011, 47, 131; and references therein. [3] J. Hunger, M. Borna, R. Kniep, J. Solid State Chem., 2010, 182, 702; J. Hunger, M. Borna, R. Kniep, Z. Kristallogr. NCS, 2010, 225, 217; M. Borna, J. Hunger, R. Kniep, Z. Kristallogr. NCS, 2010, 225, 223; M. Borna, J. Hunger, R. Kniep, Z. Kristallogr. NCS, 2010, 225, 225. [4] M. Borna, J. Hunger, A. Ormeci, D. Zahn, U. Burkhardt, W. Carrillo-Cabrera, R. Cardoso-Gil, R. Kniep, J. Solid State Chem., 2011, 184, 296; [5] H. Müller-Bunz, T. Nikelski, Th. Schleid, Z. Naturforsch. B, 2003, 58, 375. [6] H. U. Bambauer, J. Weidelt, J.-St. Ysker, Z. Kristallogr., 1969, 130, 207. [7] D. de Saint-Giniez, P. Laruelle, J. Flahaut, C. R. Séances, Acad. Sci. Ser. C, 1968, 267, 1029.

It is known that boron containing compounds exhibit interesting chemical and physical properties. In the past 50 years modern preparative methods have led to an overwhelming number of different structures of novel and often unexpected boron–sulfur and boron–selenium compounds. Among all these new compounds, there was only one which comprises rare earth metal (RE), boron and heavier chalcogen, namely sulfur, the europium thioborate Eu[B2S4] [1]. Selenoborates of rare earth metals are hitherto unknown. On the other hand, rare earth oxoborates represent a well-known class of compounds [2] with a wide range of applications, especially in the field of optical materials. In addition, well-defined boron compounds containing the heavier group 16 elements are fairly difficult to prepare due to the high reactivity of in situ formed boron chalcogenides towards most container materials at elevated temperatures. The chalcogenoborates of the heavier chalcogens are sensitive against oxidation and hydrolysis and therefore have to be handled in an inert environment. Therefore, developing and optimization of preparative routes for the syntheses of pure and crystalline RE thio- and selenoborates was needed. In the course of this study, the application of different preparation routes, such as optimized high-temperature routes (HT), metathesis reactions and high-pressure high-temperature routes (Hp – HT), led to sixteen new rare earth thioborates. Their crystal structures were solved and/or refined from powder and single crystal X-ray diffraction data, while the local structure around rare earth metal was confirmed from the results of the EXAFS analyses. Quantum mechanical calculations were used within this work in order to investigate the arrangement of intrinsic vacancies on the boron sites in the crystal structures of rare earth thioborates. Thermal, magnetic and optical properties of these compounds are also discussed. The rare earth thioborates discovered during this work are the first examples of ternary thioborates containing trivalent cations. These compounds can be divided into two groups of isotypic compounds: the rare earth orthothioborates with general formula REIII[BS3] (RE = La – Nd, Sm, Gd and Tb) [3] and the rare earth thioborate sulfides with general formula REIII¦9B5S21, (RE = Gd – Lu, and Y) [4]. In the crystal structure of RE[BS3] (orthorhombic, space group Pna21, Z = 4), the sulfur atoms form the vertices of corrugated kagome nets, within which every second triangle is occupied by boron and the large hexagons are centered by RE cations. The structural features of the isotypic RE[BS3] phases show great similarities to those of rare earth oxoborates RE[BO3] and orthothioborates of alkali and alkaline earth metals as well as to thallium orthothioborate, yet pronounced differences are also observed: the [BS3]3– groups in the crystal structures of RE[BS3] are more distorted, where the distortion decreases with the decreasing size of the RE element, and the coordination environments of the [BS3]3– groups in the crystal structures of RE[BS3] are different in comparison with the coordination environments of the [BO3]3– groups in the crystal structures of λ-Nd[BO3] [5] and of o-Ce[BO3] [6]. The results of the IR and Raman investigations are in agreement with the presence of [BS3]3– anions in the crystal structure of RE[BS3]. Thermal analyses revealed the thermal stability of these compounds under inert conditions up to ~ 1200 K. Analyses of the magnetic properties of the Sm, Gd and Tb thioborates showed that both Gd and Tb phases order antiferromagnetically. The magnetic susceptibility for Sm orthothioborate approximately follows the Van-Vleck theory for Sm3+. Between 50 K and 62 K a transition appears which is independent of the magnetic field: the magnetic susceptibility becomes lower. This effect might indicate a discontinuous valence transition of Sm which was further investigated by means of XANES and X-ray diffraction using synchrotron radiation, both at low temperatures. The series of isotypic RE thioborate sulfides with composition RE9B5S21, was obtained by the application of Hp – HT conditions to starting mixtures with the initial chemical composition “REB3S6“, after careful optimization of the pressure, temperature and treatment time, as well as the composition of the starting mixtures. Their crystal structures adopt the Ce6Al3.33S14 [7] structure type (hexagonal, space group P63, Z = 2/3). The special features of the RE9B5S21 crystal structures, concerning boron site occupancies and different coordination environments of the two crystallographically independent boron sites, were investigated in more detail by means of quantum chemical calculations, electron diffraction methods, optical and X-ray absorption spectroscopy as well as by 11B NMR spectroscopy. The results obtained from these different experimental and computational methods are in good mutual agreement. The crystal structures of the RE9B5S21 compounds are characterized by two types of anions: tetrahedral [BS4]5– and trigonal planar [BS3]3– as well as [(S2–)3] units. Isolated [BS4]5– tetrahedra (all pointing with one of their apices along the polar [001] direction) represent a unique feature of the crystal structure which is observed for the first time in a thioborate compound. These tetrahedra are stacked along the three-fold rotation axes. Vacancies are located at the trigonal-planar coordinated boron site with preferred ordering –B–B––B–B–– along [001]. No superstructure is observed by means of electron diffraction methods as adjacent columns are shuffled along the c axis, giving rise to a randomly distributed vacancy pattern. Positions of the sulfur atoms within the [(S2–)3] substructure as well as planarity of the [BS3]3– units were investigated in more detail by means of quantum mechanical calculations. Results of the IR and Raman spectroscopy, as well as of the 11B NMR spectroscopy are in agreement with the presence of the boron atoms in two different coordination environments. Thermal analyses showed that compounds RE9B5S21 are stable under inert conditions up to ~ 1200 K. In accordance with the combined results of experimental and computational investigations, the chemical formula of the RE9B5S21 compounds is consistent with RE3[BS3]2[BS4]3S3. A short overview of investigations towards rare earth selenoborates, where in most of the cases only known binary rare earth selenides could be identified, is presented as well in this work. Investigations in the RE–B–Se systems were conducted by the application of different preparation routes by varying the experimental parameters and the initial compositions of the starting mixtures. Although no crystal structure of a ternary phase in these systems could be solved, there are indications that such phases exist, but further investigations are needed. [1] M. Döch, A. Hammerschmidt, B. Krebs, Z. Anorg. Allg. Chem., 2004, 630, 519. [2] H. Huppertz, Chem. Commun., 2011, 47, 131; and references therein. [3] J. Hunger, M. Borna, R. Kniep, J. Solid State Chem., 2010, 182, 702; J. Hunger, M. Borna, R. Kniep, Z. Kristallogr. NCS, 2010, 225, 217; M. Borna, J. Hunger, R. Kniep, Z. Kristallogr. NCS, 2010, 225, 223; M. Borna, J. Hunger, R. Kniep, Z. Kristallogr. NCS, 2010, 225, 225. [4] M. Borna, J. Hunger, A. Ormeci, D. Zahn, U. Burkhardt, W. Carrillo-Cabrera, R. Cardoso-Gil, R. Kniep, J. Solid State Chem., 2011, 184, 296; [5] H. Müller-Bunz, T. Nikelski, Th. Schleid, Z. Naturforsch. B, 2003, 58, 375. [6] H. U. Bambauer, J. Weidelt, J.-St. Ysker, Z. Kristallogr., 1969, 130, 207. [7] D. de Saint-Giniez, P. Laruelle, J. Flahaut, C. R. Séances, Acad. Sci. Ser. C, 1968, 267, 1029.:I INTRODUCTION ......................................................................... 7 1. Motivation and scope of the work .............................................. 9 2. Literature overview .................................................................. 11 2.1. The binary subsystems of the ternary systems RE–B–Q (RE = rare earth metals, Y; Q = S, Se) ......................................................... 12 2.1.1. RE–Q ............................................................................... 12 2.1.2. RE–B ............................................................................... 19 2.1.3. B–Q ................................................................................. 22 2.2. Related ternary compounds ................................................... 25 2.2.1. RE oxoborates .................................................................. 25 2.2.2. Thio- and selenoborates of alkaline, alkaline earth, transition and post transition metals ......................................................................... 33 2.2.3. The RE thioborate Eu[B2S4]................................................ 45 II PREPARATIVE METHODS AND EXPERIMENTAL TECHNIQUES .......... 47 1. Starting materials and their characterization ............................... 49 2. Synthetic approaches and optimizations .................................... 51 2.1. High-temperature routes ...................................................... 52 2.2. Metathesis reactions ............................................................ 53 2.3. Spark Plasma Sintering (SPS) ............................................... 54 2.4. High-Pressure High-Temperature (Hp – HT) Syntheses ........... 55 3. Analytical methods and samples characterization ....................... 55 3.1. Powder X-ray diffraction ...................................................... 55 3.2. Crystal structure investigations using synchrotron radiation .... 57 3.3. Single crystal X-ray diffraction analysis .................................. 57 3.4. Metallographic investigations ................................................ 58 3.5. Electron microscopy ............................................................ 58 3.5.1. Scanning electron microscopy and energy dispersive X-ray spectroscopy ............................................................................ 58 3.5.2. Transmission electron microscopy ...................................... 59 3.6. Optical spectroscopy ........................................................... 59 3.6.1. Infra-Red spectroscopy .................................................... 59 3.6.2. Raman spectroscopy ........................................................ 60 3.7. X-ray absorption spectroscopy ............................................ 60 3.8. Thermal analysis ................................................................. 62 3.9. Magnetic susceptibility measurements ................................... 63 3.10. 11B NMR spectroscopy ..................................................... 63 3.11. Quantum chemical calculations ........................................... 64 3.11.1. Total energy calculations ................................................ 64 3.11.2. Charge transfer analysis ................................................ 64 3.11.3. Chemical bonding........................................................... 64 III RARE EARTH THIOBORATES ................................................. 67 1. Reinvestigation of the only reported rare earth thioborate – EuB2S4 ....69 2. RE[BS3] (RE = La – Nd, Sm, Gd, Tb) .................................... 69 2.1. Syntheses and phase analyses .......................................... 70 2.2. Crystal structure determinations ........................................ 74 2.3. X-ray absorption spectroscopy: EXAFS data analysis for Pr[BS3] ..... 79 2.4. Crystal chemistry .............................................................. 80 2.5. Optical spectroscopy ......................................................... 83 2.6. Thermal analysis ............................................................... 86 2.7. Magnetic susceptibility ....................................................... 88 2.8. X-ray absorption spectroscopy: XANES data analysis for Sm[BS3] .. 91 2.9. Crystal structure investigation at low temperature using synchrotron radiation ................................................................................... 91 2.10. Summary ......................................................................... 95 3. Gd[BS3] : Ce, Eu, Tb ............................................................. 97 3.1. Syntheses and phase analyses ............................................. 97 3.2. Crystal structure determinations ......................................... 101 3.3. Crystal chemistry .............................................................. 103 3.4. Optical spectroscopy ......................................................... 104 3.5. Thermal analysis ............................................................... 106 3.6. Summary ......................................................................... 107 4. RE9B5S21 (RE = Tb – Lu, Y) ................................................ 107 4.1. Syntheses and phase analyses ........................................... 108 4.2. Crystal structure determinations ........................................ 109 4.3. Crystal chemistry .............................................................. 112 4.4. Electronic structure, charge transfer and chemical bonding .... 115 4.5. X-ray absorption spectroscopy: EXAFS data analysis for Lu9B5S21 .............................................................................. 119 4.6. Thermal analysis ............................................................... 121 4.7. 11B NMR investigations ..................................................... 122 4.8. Optical spectroscopy ......................................................... 123 4.9. Summary ......................................................................... 126 IV ON THE WAY TO RARE EARTH SELENOBORATES .................... 127 1. Towards ternary phases in the systems RE–B–Se, with RE = Sm, Tb – Lu.......................................................................................... 129 2. The system La–B–Se ........................................................... 134 3. The system Gd–B–Se .......................................................... 136 4. The system Y–B–Se ............................................................ 137 5. Summary ........................................................................... 139 V SUMMARY AND OUTLOOK ..................................................... 141 VI APPENDIX .......................................................................... 149 VII REFERENCES .................................................................... 163 VIII LIST OF FIGURES ............................................................. 181 IX LIST OF TABLES ................................................................ 193 X CURRICULUM VITAE ........................................................... 199 XI VERSICHERUNG ............................................................... 203

The thesis is dedicated to the approximation of high-dimensional functions from scattered data nodes. Many methods in this area lack the property of interpretability in the context of explainable artificial intelligence. The idea is to address this shortcoming by proposing a new method that is intrinsically designed around interpretability. The multivariate analysis of variance (ANOVA) decomposition is the main tool to achieve this purpose. We study the connection between the ANOVA decomposition and orthonormal bases to obtain a powerful basis representation. Moreover, we focus on functions that are mostly explained by low-order interactions to circumvent the curse of dimensionality in its exponential form. Through the connection with grouped index sets, we can propose a least-squares approximation idea via iterative LSQR. Here, the proposed grouped transformations provide fast algorithms for multiplication with the appearing matrices. Through global sensitivity indices we are then able to analyze the approximation which can be used in improving it further. The method is also well-suited for the approximation of real data sets where the sparsity-of-effects principle ensures a low-dimensional structure. We demonstrate the applicability of the method in multiple numerical experiments with real and synthetic data.:1 Introduction 2 The Classical ANOVA Decomposition 3 Fast Multiplication with Grouped Transformations 4 High-Dimensional Explainable ANOVA Approximation 5 Numerical Experiments with Synthetic Data 6 Numerical Experiments with Real Data 7 Conclusion Bibliography / Die Arbeit widmet sich der Approximation von hoch-dimensionalen Funktionen aus verstreuten Datenpunkten. In diesem Bereich leiden vielen Methoden darunter, dass sie nicht interpretierbar sind, was insbesondere im Kontext von Explainable Artificial Intelligence von großer Wichtigkeit ist. Um dieses Problem zu adressieren, schlagen wir eine neue Methode vor, die um das Konzept von Interpretierbarkeit entwickelt ist. Unser wichtigstes Werkzeug dazu ist die Analysis of Variance (ANOVA) Zerlegung. Wir betrachten insbesondere die Verbindung der ANOVA Zerlegung zu orthonormalen Basen und erhalten eine wichtige Reihendarstellung. Zusätzlich fokussieren wir uns auf Funktionen, die hauptsächlich durch niedrig-dimensionale Variableninteraktionen erklärt werden. Dies hilft uns, den Fluch der Dimensionen in seiner exponentiellen Form zu überwinden. Über die Verbindung zu Grouped Index Sets schlagen wir dann eine kleinste Quadrate Approximation mit dem iterativen LSQR Algorithmus vor. Dabei liefern die vorgeschlagenen Grouped Transformations eine schnelle Multiplikation mit den entsprechenden Matrizen. Unter Zuhilfenahme von globalen Sensitvitätsindizes können wir die Approximation analysieren und weiter verbessern. Die Methode ist zudem gut dafür geeignet, reale Datensätze zu approximieren, wobei das sparsity-of-effects Prinzip sicherstellt, dass wir mit niedrigdimensionalen Strukturen arbeiten. Wir demonstrieren die Anwendbarkeit der Methode in verschiedenen numerischen Experimenten mit realen und synthetischen Daten.:1 Introduction 2 The Classical ANOVA Decomposition 3 Fast Multiplication with Grouped Transformations 4 High-Dimensional Explainable ANOVA Approximation 5 Numerical Experiments with Synthetic Data 6 Numerical Experiments with Real Data 7 Conclusion Bibliography

Nanokristalle werden beispielsweise für eine Anwendung in Solarzellen, Lichtemittern und nichtflüchtigen Datenspeichern diskutiert. Damit diese Anwendungen funktionieren können, ist eine genaue Kontrolle der Kristallitgröße sowie der Flächendichte und Lage der Kristallite in der Matrix wichtig. Zudem sollte die Matrix amorph sein, da amorphe Matrixmaterialien die Nanokristall-Oberfläche besser passivieren und beständiger gegen Leckströme sind. In dieser Arbeit werden Ge-Nanokristalle in die Hoch-Epsilon-Dielektrika ZrO2 und TaZrOx eingebettet. Im System Ge/ZrO2 kristallisieren die Ge-Cluster und die ZrO2-Matrix bei der gleichen Temperatur. Aufgrund der kristallinen Matrix weicht die Form der Ge-Nanokristalle von einer Kugel ab, worunter unter anderem die Größenkontrolle leidet. Die Beimischung von Ta2O5 stabilisiert die amorphe Phase des ZrO2 und verhindert dadurch die gemeinsame Kristallisation. Dadurch wird es im System Ge/TaZrOx möglich, kugelförmige Ge-Nanokristalle im Größenbereich von 3 nm bis 6 nm positionskontrolliert in eine amorphe Matrix einzubetten. Für die Untersuchung einer möglichen Anwendung des Materialsystems wurden Speicherzellen eines nichtflüchtigen Datenspeichers auf Basis von Ge-Nanokristallen hergestellt. Dabei zeigte sich, dass das System Ge/TaZrOx überdurchschnittlich viele Ladungen speichert und daher für diese Anwendung vielversprechend ist. Zudem stabilisiert die Beimischung von Ta2O5 eine extrem seltene orthorhombische Modifikation des ZrO2. Für ferroelektrische Datenspeicher könnte diese Phase eine aussichtsreiche Alternative zum HfO2 sein.

Diese Arbeit beschäftigt sich mit dem Einfluss der Zugabe bestimmter Metalloxide ins Glassystem Magnesiumalumosilikate auf den spezifischen E-Modul der Gläser und die daraus hergestellten Glasfasern (GF) sowie mit dem Einsatz dieser GF in Verbundbaustoffe (GFK). 36 Gläser wurden geschmolzen und hinsichtlich Dichte und E-Modul untersucht. Die besten vier Gläser wurden thermisch charakterisiert und zu GF gezogen. Die textil-physikalischen und die mechanischen Eigenschaften dieser GF zeigten, dass die T9-GF mit 14 Gew.-% Y2O3 die besten Ergebnisse mit etwa 31,2 % höherer Zugfestigkeit und 25 % höherem E-Modul sowie eine Steigerung um 17,6 % beim spezifischen E-Modul im Vergleich zu E-GF nachwiesen. Die V10-GF besaßen mit 1993 MPa die höchste charakteristische Zugfestigkeit und wurden für Direktrovings (DR) und unidirektionale Gelege (UD) eingesetzt. Die V10-GFK Stäbe nach DIN EN ISO 9163 wiesen fast die doppelte Zugfestigkeit von E- DR-GFK auf, mit einer 23,8 %igen E-Modulsteigerung. Nach DIN EN 2747 wurden V10-UD-GFK auf Zugfestigkeit geprüft und damit die Beobachtungen aus den DR-GFK Tests bestätigt. Bezüglich der Biegeprüfungen nach DIN EN ISO 14125 wiesen die V10-UD-GFK eine um 51,8 % höhere Festigkeit als die E-UD-GFK sowie einen um 48,4 % höheren Biegemodul auf.:1 Einleitung und Motivation 8 2 Grundlagen 12 2.1 Glas als Werkstoff 12 2.1.1 Definition 12 2.1.2 Struktur des Glases und Netzwerktheorie 13 2.1.3 Glas- und Glasfasereigenschaften: 15 2.2 Glasfasern 29 2.2.1 Glasfaserherstellung 29 2.2.2 Rohstoff für die Glasfaserherstellung 35 2.2.3 Glasfasereigenschaften und -typen 37 2.2.4 Schlichte 40 2.2.5 Literaturübersicht über Hoch-Modul Glasfasern (HM-GF) 41 3 Experimentelles 46 3.1 Glasauswahl 46 3.2 Berechnung der Glaseigenschaften 49 3.3 Glasherstellung und Glasfaserziehverfahren 50 3.3.1 Gemengevorbereitung und Glasschmelzen 50 3.3.2 Ziehprozess und Düsengeometrie 51 3.4 Herstellung der Verbundhalbzeuge 53 3.5 Charakterisierungsmethoden 60 3.5.1 Dichtebestimmung 60 3.5.2 E-Modulbestimmung am Massivglas 60 3.5.3 Bestimmung der thermischen Eigenschaften: Tg ,TL,ⴄ 62 3.5.4 Zugfestigkeit und E-Modulbestimmung von einzelnen Filamenten 66 3.5.5 Verbundeigenschaften Charakterisierung 68 4 Ergebnisse und Diskussion 70 4.1 Glasherstellung und Eigenschaften 70 4.1.1 Glasschmelzen 70 4.1.2 Dichte und E-Modul 73 4.1.3 Thermische Eigenschaften 82 4.2 Glasfaserherstellung und Charakterisierung 86 4.2.1 GF-Herstellung 86 4.2.2 GF-Charakterisierung 87 4.3 Einsatz der GF in Verbundstoffen 93 4.3.1 Die Pull-Out Versuche und deren Ergebnisse 93 4.3.2 GFK-Stäbe Herstellung und Charakterisierung 97 4.3.3 UD-Laminate Herstellung und Charakterisierung 104 4.4 Technische und wirtschaftliche Diskussion der Ergebnisse 108 5 Zusammenfassung und Ausblick 111 6 Danksagung 116 7 Abbildungsverzeichnis 118 8 Tabellenverzeichnis 121 9 Literaturverzeichnis 122 10 Anlagen 131 / This thesis investigates the influence of the addition of certain metal oxides to the magnesium aluminosilicate glass system on the specific E-Modulus of the glasses and the glass fibres (GF) made from them, as well as the use of these GF in composites (GFRP). 36 glasses were melted and analysed for density and E-Modulus. The best four glasses were then thermally characterized and drawn into GF. The textile physical and mechanical properties of these GF showed that the T9-GF with 14 wt.% Y2O3 offered, with about 31.2 % higher tensile strength and 25 % higher E-Modulus as well as an increase of 17.6 % in specific E-Modulus, the best results compared to E-GF. The V10-GF possessed the highest characteristic tensile strength of 1993 MPa and were used to produce non-crimp unidirectional fabrics (UD) and direct rovings (DR) for GFRP-production. The tensile strength of the V10-DR-GFRP according to DIN EN ISO 9163 was almost twice that of E-DR-GFRP with a 23.8 % increase in the E-Modulus. According to DIN EN 2747, V10-UD-GFRP was tested for tensile strength and the observations from the test on DR-GFRP were validated. Regarding the flexural tests according to DIN EN ISO 14125, the V10-UD-GFRP showed a 51.8 % higher strength than the E-UD-GFRP as well as a 48.4 % higher flexural modulus.:1 Einleitung und Motivation 8 2 Grundlagen 12 2.1 Glas als Werkstoff 12 2.1.1 Definition 12 2.1.2 Struktur des Glases und Netzwerktheorie 13 2.1.3 Glas- und Glasfasereigenschaften: 15 2.2 Glasfasern 29 2.2.1 Glasfaserherstellung 29 2.2.2 Rohstoff für die Glasfaserherstellung 35 2.2.3 Glasfasereigenschaften und -typen 37 2.2.4 Schlichte 40 2.2.5 Literaturübersicht über Hoch-Modul Glasfasern (HM-GF) 41 3 Experimentelles 46 3.1 Glasauswahl 46 3.2 Berechnung der Glaseigenschaften 49 3.3 Glasherstellung und Glasfaserziehverfahren 50 3.3.1 Gemengevorbereitung und Glasschmelzen 50 3.3.2 Ziehprozess und Düsengeometrie 51 3.4 Herstellung der Verbundhalbzeuge 53 3.5 Charakterisierungsmethoden 60 3.5.1 Dichtebestimmung 60 3.5.2 E-Modulbestimmung am Massivglas 60 3.5.3 Bestimmung der thermischen Eigenschaften: Tg ,TL,ⴄ 62 3.5.4 Zugfestigkeit und E-Modulbestimmung von einzelnen Filamenten 66 3.5.5 Verbundeigenschaften Charakterisierung 68 4 Ergebnisse und Diskussion 70 4.1 Glasherstellung und Eigenschaften 70 4.1.1 Glasschmelzen 70 4.1.2 Dichte und E-Modul 73 4.1.3 Thermische Eigenschaften 82 4.2 Glasfaserherstellung und Charakterisierung 86 4.2.1 GF-Herstellung 86 4.2.2 GF-Charakterisierung 87 4.3 Einsatz der GF in Verbundstoffen 93 4.3.1 Die Pull-Out Versuche und deren Ergebnisse 93 4.3.2 GFK-Stäbe Herstellung und Charakterisierung 97 4.3.3 UD-Laminate Herstellung und Charakterisierung 104 4.4 Technische und wirtschaftliche Diskussion der Ergebnisse 108 5 Zusammenfassung und Ausblick 111 6 Danksagung 116 7 Abbildungsverzeichnis 118 8 Tabellenverzeichnis 121 9 Literaturverzeichnis 122 10 Anlagen 131

The elucidation of the composition and organization of genomes of higher plants is a fundamental problem of modern molecular biology. The genus Beta containing 14 species assigned to the sections Beta, Corollinae, Nanae and Procumbentes provides a suitable system for the comparative study of the nuclear genomes. Sugar beet Beta vulgaris has a genome size of 758 Mbp DNA with estimated 63 % repetitive sequences and the number of chromosomes n=9. The wild beet Beta procumbens is an important natural pool of resistance against pests and tolerance to unfavorable growth conditions. The subject of this research was the isolation and description of new repetitive DNA families from genomes of this Beta species. This work presents the molecular investigation and cytogenetic characterization by high-resolution multicolor fluorescent in situ hybridization (FISH) of the satellite and dispersed repetitive sequences in wild and cultivated beet species and in their hybrids. New repetitive sequences were isolated from the B. procumbens genome. The AluI restriction satellite repeats pAp11 are 229-246 bp long and form subfamilies. The satellite is amplified in the section Procumbentes, but also found in distantly related section Beta. Thus, pAp11 is probably an ancient component of Beta genomes. It could be the ancestor of the satellite subfamily pEV4 in B. vulgaris based on sequence analysis, Southern hybridization and comparative FISH. pAp11 was found at centromeric and a few intercalary sites in B. procumbens and formed intercalary blocks on B. vulgaris chromosomes where it co-localized with pEV4. These remarkable differences in the chromosomal position of pAp11 between Procumbentes and Beta species indicate that both satellites were likely involved in the expansion or rearrangement of the intercalary heterochromatin of B. vulgaris. Other two sequence families characterized on molecular, genomic and chromosomal levels are the non-homologous repeats pAp4 and pAp22, 1354 and 582 bp long. They have a dispersed organization in the genome and are widely scattered along B. procumbens chromosomes. pAp4 and pAp22 are specific for the section Procumbentes and can be used as DNA probes to discriminate parental genomes in interspecific hybrids. High-resolution FISH on meiotic chromosomes showed that the both sequences mostly co-localize. The PCR analysis of their flanking regions revealed that pAp22 is a part of a Long Terminal Repeat (LTR) of an Athila-like env-class retrotransposon. This is the first indication that the retrovirus-like DNA elements exist in Beta. An ancient family of subtelomeric satellite DNA pAv34 was isolated from all four sections of the genus Beta and from spinach, a related Chenopodiaceae. Five clones were analyzed from each of the five species. The genomic organization and species distribution of the satellites were studied by sequencing and Southern hybridization. The repeating units in all families are 344-362 bp long and share 46.2-98.8 % similarity. Each monomer consists of two subunits SU1 and SU2 of 165-184 bp. The maximum likelihood and neighbor joining analyses of the 25 subtelomeric satellite monomers and their subunits indicated, that the duplication leading to the emergence of the 360 bp satellite should have occurred early in the phylogeny. The two directions of diversification are the clustering of satellites in two groups of subunits SU1 and SU2 and the arrangement of satellite repeats in section-specific groups. The comparative chromosomal localization of the telomeric repeat, pAv34 and rDNA was investigated by multicolor FISH. B. vulgaris chromosome termini showed unique physical organization of telomeric repeat and the subtelomeric satellite, as studied by high-resolution FISH on extended DNA fibers. The estimated length of the telomeric array was 0.55 - 62.65 kb, the length of pAv34 was 5.0-125.25 kb, the spacer between these sequences spanned 1.0-16.60 kb. Eight various classes of repeats were used to characterize the minichromosomes of the sugar beet fragment addition lines PRO1 and PAT2 by comparative multi-color FISH. The study allowed to propose a schematic pattern of repetitive DNA organization on the PRO1 and PAT2 minichromosomes. PRO1 has an acrocentric minichromosome, while PAT2 possesses a metacentric or submetacentric chromosome fragment. The functional integrity of the fragment addition line centromeres was confirmed by an immunostaining localization of the proteins specific to the active kinetochore. The serine 10-phosphorylated histone H3 was detected in pericentromeric regions of the PRO1 chromosomes. The microtubuli attachment sites were visualized as parts of kinetochore complexes.

This work presents different novel gate drive unit (GDU) concepts for IGBT and reverse conducting IGBT (RC-IGBT). They have been experimentally tested with medium voltage class IGBT modules (1200...1700V/650…1400A) and a RC-IGBT module (1200V/200A). The switching behaviour of the RC-IGBT was investigated, and a new trigger pulse pattern to drive the RC-IGBT was developed, designed and implemented. The experimental results showed that the switching losses were reduced by 20% in the RC-IGBT compared to the switching losses of a standard diode. Two novel schemes are introduced to estimate the collector current through the IGBT, based on the measurement of the voltage across the internal stray inductance of the IGBT module. Furthermore, a GDU concept was derived to balance the on-state collector currents of parallel-connected IGBTs, reducing the current imbalance to 5%. Also, a new fast short circuit protection method (FSCP) for IGBT modules was developed, designed and implemented in another GDU, allowing turning-off the considered IGBT in less than 1μs, reducing the IGBT stress. Another scheme implemented in a GDU features an improved gate current switching profile of the IGBT, which reduces the switching losses by 25% compared to the standard switching method. In order to reduce the conduction losses, a GDU with an increased turn-on gate-emitter voltage (larger than 20 V) was investigated. In the investigated IGBT, the on-state losses were reduced by 18% when a gate-emitter voltage of 35V is used compared to when a gate-emitter voltage of 15V is used. All these new GDU concepts have been implemented with a simple and inexpensive electronic circuitry, which is an important feature for a possible industrial implementation.

This work presents different novel gate drive unit (GDU) concepts for IGBT and reverse conducting IGBT (RC-IGBT). They have been experimentally tested with medium voltage class IGBT modules (1200...1700V/650…1400A) and a RC-IGBT module (1200V/200A). The switching behaviour of the RC-IGBT was investigated, and a new trigger pulse pattern to drive the RC-IGBT was developed, designed and implemented. The experimental results showed that the switching losses were reduced by 20% in the RC-IGBT compared to the switching losses of a standard diode. Two novel schemes are introduced to estimate the collector current through the IGBT, based on the measurement of the voltage across the internal stray inductance of the IGBT module. Furthermore, a GDU concept was derived to balance the on-state collector currents of parallel-connected IGBTs, reducing the current imbalance to 5%. Also, a new fast short circuit protection method (FSCP) for IGBT modules was developed, designed and implemented in another GDU, allowing turning-off the considered IGBT in less than 1μs, reducing the IGBT stress. Another scheme implemented in a GDU features an improved gate current switching profile of the IGBT, which reduces the switching losses by 25% compared to the standard switching method. In order to reduce the conduction losses, a GDU with an increased turn-on gate-emitter voltage (larger than 20 V) was investigated. In the investigated IGBT, the on-state losses were reduced by 18% when a gate-emitter voltage of 35V is used compared to when a gate-emitter voltage of 15V is used. All these new GDU concepts have been implemented with a simple and inexpensive electronic circuitry, which is an important feature for a possible industrial implementation.

The elucidation of the composition and organization of genomes of higher plants is a fundamental problem of modern molecular biology. The genus Beta containing 14 species assigned to the sections Beta, Corollinae, Nanae and Procumbentes provides a suitable system for the comparative study of the nuclear genomes. Sugar beet Beta vulgaris has a genome size of 758 Mbp DNA with estimated 63 % repetitive sequences and the number of chromosomes n=9. The wild beet Beta procumbens is an important natural pool of resistance against pests and tolerance to unfavorable growth conditions. The subject of this research was the isolation and description of new repetitive DNA families from genomes of this Beta species. This work presents the molecular investigation and cytogenetic characterization by high-resolution multicolor fluorescent in situ hybridization (FISH) of the satellite and dispersed repetitive sequences in wild and cultivated beet species and in their hybrids. New repetitive sequences were isolated from the B. procumbens genome. The AluI restriction satellite repeats pAp11 are 229-246 bp long and form subfamilies. The satellite is amplified in the section Procumbentes, but also found in distantly related section Beta. Thus, pAp11 is probably an ancient component of Beta genomes. It could be the ancestor of the satellite subfamily pEV4 in B. vulgaris based on sequence analysis, Southern hybridization and comparative FISH. pAp11 was found at centromeric and a few intercalary sites in B. procumbens and formed intercalary blocks on B. vulgaris chromosomes where it co-localized with pEV4. These remarkable differences in the chromosomal position of pAp11 between Procumbentes and Beta species indicate that both satellites were likely involved in the expansion or rearrangement of the intercalary heterochromatin of B. vulgaris. Other two sequence families characterized on molecular, genomic and chromosomal levels are the non-homologous repeats pAp4 and pAp22, 1354 and 582 bp long. They have a dispersed organization in the genome and are widely scattered along B. procumbens chromosomes. pAp4 and pAp22 are specific for the section Procumbentes and can be used as DNA probes to discriminate parental genomes in interspecific hybrids. High-resolution FISH on meiotic chromosomes showed that the both sequences mostly co-localize. The PCR analysis of their flanking regions revealed that pAp22 is a part of a Long Terminal Repeat (LTR) of an Athila-like env-class retrotransposon. This is the first indication that the retrovirus-like DNA elements exist in Beta. An ancient family of subtelomeric satellite DNA pAv34 was isolated from all four sections of the genus Beta and from spinach, a related Chenopodiaceae. Five clones were analyzed from each of the five species. The genomic organization and species distribution of the satellites were studied by sequencing and Southern hybridization. The repeating units in all families are 344-362 bp long and share 46.2-98.8 % similarity. Each monomer consists of two subunits SU1 and SU2 of 165-184 bp. The maximum likelihood and neighbor joining analyses of the 25 subtelomeric satellite monomers and their subunits indicated, that the duplication leading to the emergence of the 360 bp satellite should have occurred early in the phylogeny. The two directions of diversification are the clustering of satellites in two groups of subunits SU1 and SU2 and the arrangement of satellite repeats in section-specific groups. The comparative chromosomal localization of the telomeric repeat, pAv34 and rDNA was investigated by multicolor FISH. B. vulgaris chromosome termini showed unique physical organization of telomeric repeat and the subtelomeric satellite, as studied by high-resolution FISH on extended DNA fibers. The estimated length of the telomeric array was 0.55 - 62.65 kb, the length of pAv34 was 5.0-125.25 kb, the spacer between these sequences spanned 1.0-16.60 kb. Eight various classes of repeats were used to characterize the minichromosomes of the sugar beet fragment addition lines PRO1 and PAT2 by comparative multi-color FISH. The study allowed to propose a schematic pattern of repetitive DNA organization on the PRO1 and PAT2 minichromosomes. PRO1 has an acrocentric minichromosome, while PAT2 possesses a metacentric or submetacentric chromosome fragment. The functional integrity of the fragment addition line centromeres was confirmed by an immunostaining localization of the proteins specific to the active kinetochore. The serine 10-phosphorylated histone H3 was detected in pericentromeric regions of the PRO1 chromosomes. The microtubuli attachment sites were visualized as parts of kinetochore complexes.