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Die vorliegende Arbeit mit dem Titel „Eine Frage der Zeit. Wie Einflüsse individueller Merkmale auf Einkommen bei Frauen über ihre familiären Verpflichtungen vermittelt werden“ geht der Frage der Heterogenität bei weiblichen Einkommensergebnissen nach. Dabei steht die Thematik der individuellen Investitionen in die familiäre Arbeit als erklärender Faktor im Vordergrund und es wird der Frage nachgegangen, warum die einen Frauen viele und andere weniger häusliche Verpflichtungen übernehmen. Hierfür werden das individuelle Humankapital der Frauen, ihre Werteorientierungen und individuelle berufliche Motivationen aus der Jugendzeit und im Erwachsenenalter herangezogen. Die analysierten Daten (Daten der LifE-Studie) repräsentieren eine Langzeitperspektive vom 16. bis zum 45. Lebensjahr der befragten Frauen. Zusammenfassend kann im Ergebnis gezeigt werden, dass ein Effekt familiärer Verpflichtungen auf Einkommensergebnisse bei Frauen im frühen und mittleren Erwachsenenalter als Zeiteffekt über die investierte Erwerbsarbeitszeit vermittelt wird. Die Relevanz privater Routinearbeiten für Berufserfolge von Frauen und insbesondere Müttern stellt somit eine Frage der Zeit dar. Weiterhin kann für individuelle Einflüsse auf Einkommen bei Frauen gezeigt werden, dass höhere zeitliche Investitionen in den Beruf von Frauen mit hohem Bildungsniveau als indirect-only-Mediation nur über die Umverteilung häuslicher Arbeiten erklärbar werden. Frauen sind demnach zwar Gewinnerinnen der Bildungsexpansion. Die Bildungsexpansion stellt jedoch auch die Geschichte der Entstehung eines Vereinbarkeitskonflikts für eben diese Frauen dar, weil die bis heute virulenten Beharrungskräfte hinsichtlich der Frauen zugeschriebenen familiären Verpflichtungen mit ihren gestiegenen beruflichen Erwartungen und Chancen kollidieren. Die Arbeit leistet in ihren Analyseresultaten einen wichtigen Beitrag zur Erklärung heterogener Investitionen von Frauen in den Beruf und ihrer Einkommensergebnisse aus dem Privaten heraus.
In this work the human AOX1 was characterized and detailed aspects regarding the expression, the enzyme kinetics and the production of reactive oxygen species (ROS) were investigated. The hAOX1 is a cytosolic enzyme belonging to the molybdenum hydroxylase family. Its catalytically active form is a homodimer with a molecular weight of 300 kDa. Each monomer (150 kDa) consists of three domains: a N-terminal domain (20 kDa) containing two [2Fe-2S] clusters, a 40 kDa intermediate domain containing a flavin adenine dinucleotide (FAD), and a C-terminal domain (85 kDa) containing the substrate binding pocket and the molybdenum cofactor (Moco). The hAOX1 has an emerging role in the metabolism and pharmacokinetics of many drugs, especially aldehydes and N- heterocyclic compounds.
In this study, the hAOX1 was hetereogously expressed in E. coli TP1000 cells, using a new codon optimized gene sequence which improved the expressed protein yield of around 10-fold compared to the previous expression systems for this enzyme. To increase the catalytic activity of hAOX1, an in vitro chemical sulfuration was performed to favor the insertion of the equatorial sulfido ligand at the Moco with consequent increased enzymatic activity of around 10-fold. Steady-state kinetics and inhibition studies were performed using several substrates, electron acceptors and inhibitors. The recombinant hAOX1 showed higher catalytic activity when molecular oxygen was used as electron acceptor. The highest turn over values were obtained with phenanthridine as substrate. Inhibition studies using thioridazine (phenothiazine family), in combination with structural studies performed in the group of Prof. M.J. Romão, Nova Universidade de Lisboa, showed a new inhibition site located in proximity of the dimerization site of hAOX1. The inhibition mode of thioridazine resulted in a noncompetitive inhibition type. Further inhibition studies with loxapine, a thioridazine-related molecule, showed the same type of inhibition. Additional inhibition studies using DCPIP and raloxifene were carried out.
Extensive studies on the FAD active site of the hAOX1 were performed. Twenty new hAOX1 variants were produced and characterized. The hAOX1 variants generated in this work were divided in three groups: I) hAOX1 single nucleotide polymorphisms (SNP) variants; II) XOR- FAD loop hAOX1 variants; III) additional single point hAOX1 variants. The hAOX1 SNP variants G46E, G50D, G346R, R433P, A439E, K1231N showed clear alterations in their catalytic activity, indicating a crucial role of these residues into the FAD active site and in relation to the overall reactivity of hAOX1.
Furthermore, residues of the bovine XOR FAD flexible loop (Q423ASRREDDIAK433) were introduced in the hAOX1. FAD loop hAOX1 variants were produced and characterized for their stability and catalytic activity. Especially the variants hAOX1 N436D/A437D/L438I, N436D/A437D/L438I/I440K and Q434R/N436D/A437D/L438I/I440K showed decreased catalytic activity and stability. hAOX1 wild type and variants were tested for reactivity toward NADH but no reaction was observed.
Additionally, the hAOX1 wild type and variants were tested for the generation of reactive oxygen species (ROS). Interestingly, one of the SNP variants, hAOX1 L438V, showed a high ratio of superoxide prodction. This result showed a critical role for the residue Leu438 in the mechanism of oxygen radicals formation by hAOX1. Subsequently, further hAOX1 variants having the mutated Leu438 residue were produced. The variants hAOX1 L438A, L438F and L438K showed superoxide overproduction of around 85%, 65% and 35% of the total reducing equivalent obtained from the substrate oxidation.
The results of this work show for the first time a characterization of the FAD active site of the hAOX1, revealing the importance of specific residues involved in the generation of ROS and effecting the overall enzymatic activity of hAOX1. The hAOX1 SNP variants presented here indicate that those allelic variations in humans might cause alterations ROS balancing and clearance of drugs in humans.
Nowadays, the need to protect the environment becomes more urgent than ever. In the field of chemistry, this translates to practices such as waste prevention, use of renewable feedstocks, and catalysis; concepts based on the principles of green chemistry. Polymers are an important product in the chemical industry and are also in the focus of these changes. In this thesis, more sustainable approaches to make two classes of polymers, polypeptoids and polyesters, are described.
Polypeptoids or poly(alkyl-N-glycines) are isomers of polypeptides and are biocompatible, as well as degradable under biologically relevant conditions. In addition to that, they can have interesting properties such as lower critical solution temperature (LCST) behavior. They are usually synthesized by the ring opening polymerization (ROP) of N-carboxy anhydrides (NCAs), which are produced with the use of toxic compounds (e.g. phosgene) and which are highly sensitive to humidity. In order to avoid the direct synthesis and isolation of the NCAs, N-phenoxycarbonyl-protected N-substituted glycines are prepared, which can yield the NCAs in situ. The conditions for the NCA synthesis and its direct polymerization are investigated and optimized for the simplest N-substituted glycine, sarcosine. The use of a tertiary amine in less than stoichiometric amounts compared to the N-phenoxycarbonyl--sarcosine seems to accelerate drastically the NCA formation and does not affect the efficiency of the polymerization. In fact, well defined polysarcosines that comply to the monomer to initiator ratio can be produced by this method. This approach was also applied to other N-substituted glycines.
Dihydroxyacetone is a sustainable diol produced from glycerol, and has already been used for the synthesis of polycarbonates. Here, it was used as a comonomer for the synthesis of polyesters. However, the polymerization of dihydroxyacetone presented difficulties, probably due to the insolubility of the macromolecular chains. To circumvent the problem, the dimethyl acetal protected dihydroxyacetone was polymerized with terephthaloyl chloride to yield a soluble polymer. When the carbonyl was recovered after deprotection, the product was insoluble in all solvents, showing that the carbonyl in the main chain hinders the dissolution of the polymers. The solubility issue can be avoided, when a 1:1 mixture of dihydroxyacetone/ ethylene glycol is used to yield a soluble copolyester.
Self-adaptive data quality
(2017)
Carrying out business processes successfully is closely linked to the quality of the data inventory in an organization. Lacks in data quality lead to problems: Incorrect address data prevents (timely) shipments to customers. Erroneous orders lead to returns and thus to unnecessary effort. Wrong pricing forces companies to miss out on revenues or to impair customer satisfaction. If orders or customer records cannot be retrieved, complaint management takes longer. Due to erroneous inventories, too few or too much supplies might be reordered.
A special problem with data quality and the reason for many of the issues mentioned above are duplicates in databases. Duplicates are different representations of same real-world objects in a dataset. However, these representations differ from each other and are for that reason hard to match by a computer. Moreover, the number of required comparisons to find those duplicates grows with the square of the dataset size. To cleanse the data, these duplicates must be detected and removed. Duplicate detection is a very laborious process. To achieve satisfactory results, appropriate software must be created and configured (similarity measures, partitioning keys, thresholds, etc.). Both requires much manual effort and experience.
This thesis addresses automation of parameter selection for duplicate detection and presents several novel approaches that eliminate the need for human experience in parts of the duplicate detection process.
A pre-processing step is introduced that analyzes the datasets in question and classifies their attributes semantically. Not only do these annotations help understanding the respective datasets, but they also facilitate subsequent steps, for example, by selecting appropriate similarity measures or normalizing the data upfront. This approach works without schema information.
Following that, we show a partitioning technique that strongly reduces the number of pair comparisons for the duplicate detection process. The approach automatically finds particularly suitable partitioning keys that simultaneously allow for effective and efficient duplicate retrieval. By means of a user study, we demonstrate that this technique finds partitioning keys that outperform expert suggestions and additionally does not need manual configuration. Furthermore, this approach can be applied independently of the attribute types.
To measure the success of a duplicate detection process and to execute the described partitioning approach, a gold standard is required that provides information about the actual duplicates in a training dataset. This thesis presents a technique that uses existing duplicate detection results and crowdsourcing to create a near gold standard that can be used for the purposes above. Another part of the thesis describes and evaluates strategies how to reduce these crowdsourcing costs and to achieve a consensus with less effort.
Die Arktis erwärmt sich schneller als der Rest der Erde. Die Auswirkungen manifestieren sich unter Anderem in einer verstärkten Erwärmung der arktischen Grenzschicht. Diese Arbeit befasst sich mit Wechselwirkungen zwischen synoptischen Zyklonen und der arktischen Atmosphäre auf lokalen bis überregionalen Skalen. Ausgangspunkt dafür sind Messdaten und Modellsimulationen für den Zeitraum der N-ICE2015 Expedition, die von Anfang Januar bis Ende Juni 2015 im arktischen Nordatlantiksektor stattgefunden hat.
Anhand von Radiosondenmessungen lassen sich Auswirkungen von synoptischen Zyklonen am deutlichsten im Winter erkennen, da sie durch die Advektion warmer und feuchter Luftmassen in die Arktis den Zustand der Atmosphäre von einem strahlungs-klaren in einen strahlungs-opaken ändern. Obwohl dieser scharfe Kontrast nur im Winter existiert, zeigt die Analyse, dass der integrierte Wasserdampf als Indikator für die Advektion von Luftmassen aus niedrigen Breiten in die Arktis auch im Frühjahr geeignet ist. Neben der Advektion von Luftmassen wird der Einfluss der Zyklonen auf die statische Stabilität charakterisiert. Beim Vergleich der N-ICE2015 Beobachtungen mit der SHEBA Kampagne (1997/1998), die über dickerem Eis stattfand, finden sich trotz der unterschiedlichen Meereisregime Ähnlichkeiten in der statischen Stabilität der Atmosphäre. Die beobachteten Differenzen in der Stabilität lassen sich auf Unterschiede in der synoptischen Aktivität zurückführen. Dies lässt vermuten, dass die dünnere Eisdecke auf saisonalen Zeitskalen nur einen geringen Einfluss auf die thermodynamische Struktur der arktischen Troposphäre besitzt, solange eine dicke Schneeschicht sie bedeckt. Ein weiterer Vergleich mit den parallel zur N-ICE2015 Kampagne gestarteten Radiosonden der AWIPEV Station in Ny-Åesund, Spitzbergen, macht deutlich, dass die synoptischen Zyklonen oberhalb der Orographie auf saisonalen Zeitskalen das Wettergeschehen bestimmen.
Des Weiteren werden für Februar 2015 die Auswirkungen von in der Vertikalen variiertem Nudging auf die Entwicklung der Zyklonen am Beispiel des hydrostatischen regionalen Klimamodells HIRHAM5 untersucht. Es zeigt sich, dass die Unterschiede zwischen den acht Modellsimulationen mit abnehmender Anzahl der genudgten Level zunehmen. Die größten Differenzen resultieren vornehmlich aus dem zeitlichen Versatz der Entwicklung synoptischer Zyklonen. Zur Korrektur des Zeitversatzes der Zykloneninitiierung genügt es bereits, Nudging in den unterstem 250 m der Troposphäre anzuwenden. Daneben findet sich zwischen den genudgten HIRHAM5-Simulation und den in situ Messungen der gleiche positive Temperaturbias, den auch ERA-Interim besitzt. Das freie HIRHAM hingegen reproduziert das positive Ende der N-ICE2015 Temperaturverteilung gut, besitzt aber einen starken negativen Bias, der sehr wahrscheinlich aus einer Unterschätzung des Feuchtegehalts resultiert. An Beispiel einer Zyklone wird gezeigt, dass Nudging Einfluss auf die Lage der Höhentiefs besitzt, die ihrerseits die Zyklonenentwicklung am Boden beeinflussen. Im Weiteren wird mittels eines für kleine Ensemblegrößen geeigneten Varianzmaßes eine statistische Einschätzung der Wirkung des Nudgings auf die Vertikale getroffen. Es wird festgestellt, dass die Ähnlichkeit der Modellsimulationen in der unteren Troposphäre generell höher ist als darüber und in 500 hPa ein lokales Minimum besitzt.
Im letzten Teil der Analyse wird die Wechselwirkung der oberen und unteren Stratosphäre anhand zuvor betrachteter Zyklonen mit Daten der ERA-Interim Reanalyse untersucht. Lage und Ausrichtung des Polarwirbels erzeugten ab Anfang Februar 2015 eine ungewöhnlich große Meridionalkomponente des Tropopausenjets, die Zugbahnen in die zentrale Arktis begünstigte. Am Beispiel einer Zyklone wird die Übereinstimmung der synoptischen Entwicklung mit den theoretischen Annahmen über den abwärts gerichteten Einfluss der Stratosphäre auf die Troposphäre hervorgehoben. Dabei spielt die nicht-lineare Wechselwirkung zwischen der Orographie Grönlands, einer Intrusion stratosphärischer Luft in die Troposphäre sowie einer in Richtung Arktis propagierender Rossby-Welle eine tragende Rolle. Als Indikator dieser Wechselwirkung werden horizontale Signaturen aus abwechselnd aufsteigender und absinkender Luft innerhalb der Troposphäre identifiziert.
The valorization of carbohydrates is one of the most promising fields in green chemistry, as it enables to produce bulk chemicals and fuels out of renewable and abundant resources, instead of further exploiting fossil feedstocks. The focus in this thesis is the conversion of fructose, using dehydration and hydrodeoxygenation reactions. The main goal is to find an easy continuous process, including the solubility of the sugar in a green solvent, the conversion over a solid acid as well as over a metal@tungsten carbide catalyst.
At the beginning of this thesis, solid acid catalysts are synthesized by using carbohydrate material like glucose and starch at high temperatures (up to 600 °C). Additionally a third carbon is synthesized, using an activation method based on Ca(OH)2. After carbonization and further sulfonation, using fuming sulfuric acid, the three resulting catalysts are characterized together with sulfonated carbon black and Amberlyst 15 as references. In order to test all solid acid catalysts in reaction, a 250 mm x 4.6 mm stainless steel column is used as a fixed-bed continuous reactor. The temperature (110 °C to 250 °C) and residence time (2 to 30 minutes) is varied, and a direct relationship between contact time and selectivity is determined. The reaction mechanism, as well as the product distribution is showing a dehydration step of fructose towards 5-hydroxymethylfurfural (HMF). These furan-ring molecules are considered as “sleeping giants”, due to the possibility of using them as fuel, but also for upgrading them to chemicals like terephthalic acid or p-xylene. Consecutive reactions are producing levulinic acid, as well as condensation products with ethanol and formic acid. The activated carbon is additionally showing a 2 % yield of 2,5-Dimethylfuran (DMF) production, pointing towards the extraordinary properties of this catalyst. Without a metal catalyst present, what is normally necessary for hydrogenation reactions, a transferhydrogenation (with formic acid) is observed. The active catalyst was therefore carbon itself, what activated the hydrogen on its surface. This phenomenon was just very rarely observed so far. Expensive noble metals are the material of choice, when it comes to hydrogenation reactions nowadays and cheaper alternatives are necessary.
By postulating a similar electronic structure of tungsten carbide (WC) to platinum by Lewy and Boudart, research is focusing on the replacement of Pt. The production of nano-sized tungsten carbide particles (7.5 ± 2.5 nm, 70 m2 g-1) is enabled by the so called “urea glass route” and its catalytic performances are compared to commercial material. It is shown, that the activity is strongly dependent on the size of the particles as well as the surface area. Nano-sized tungsten carbide is showing activity for hydrogenation reactions under mild conditions (maximum 150 °C, 30 bar). This material therefore opens up new possibilities for replacing the rare and expensive platinum with tungsten carbide based catalysts.
Additionally different metal nanoparticles of palladium, copper and nickel are deposited on top of WC to further promote its reactivity. The nickel nanoparticles are strongly connected to WC and showed the best activity as well as selectivity for upgrading HMF with hydrodeoxygenation. The Ni@WC is not leaching and is showing very good hydrodeoxygenation properties with DMF yields up to 90 percent. Copper@WC is not showing good activity and palladium@WC enables undesired consecutive reactions, hydrogenating the furan ring system.
In order to enable the upgrade of fructose to DMF directly in a continuous system, the current H CUBE Pro TM hydrogenation system is customized with a second reaction column. A 250 mm x 4.6 mm stainless steel reactor column is connected ahead of the hydrogen insertion, enabling the dehydration of fructose to HMF derivatives, before pumping these products into the second column for hydrogenation. The overall residence time in the two column reactor system is 14 minutes. The overall results are an almost full conversion with a yield of 38.5 % DMF and 47 % yield of EL. The main disadvantage is the formation of higher mass products, so called humins, which start depositing on top of the catalysts, blocking their active sites.
In general it can be stated, that a two column system goes along with a higher investment as well as more maintenance costs, compared to a one column catalytic approach. To develop a catalyst, which is on the one hand able to dehydrate as well as hydrodeoxygenate the reactants, is aimed for at the last part of the thesis. The activated carbon however shows already activity for hydrodeoxygenation without any metal present and offers itself therefore as an alternative to overcome the temperature instability of Amberlyst 15 (max. 120 °C) for a combined DMF production directly from fructose. The activity for the upgrade to DMF is increased from 2 % to 12 % DMF yield in one mixed continuous column.
In order to scale up the entire one column approach, an 800 mm x 28.5 mm inner diameter column was planned and manufactured. The system is scaled up and assembled, whereas this flow reactor system is able to be run with 50 mL min-1 maximum flow rate, to stand a pressure of maximum 100 bar and be heated to around 500 °C. The tubing and connections, as well as the used devices are planned according to be safe and easy in use. The scaled-up approach offers a reaction column 120 times bigger (510 ml) then the first extension of the commercial system. This further extension offers the possibility of ranging between 1 and 1000 mL min-1, making it possible to use the approach in pilot plant applications.
Development of a reliable and environmentally friendly synthesis for fluorescence carbon nanodots
(2017)
Carbon nanodots (CNDs) have generated considerable attention due to their promising properties, e.g. high water solubility, chemical inertness, resistance to photobleaching, high biocompatibility and ease of functionalization. These properties render them ideal for a wide range of functions, e.g. electrochemical applications, waste water treatment, (photo)catalysis, bio-imaging and bio-technology, as well as chemical sensing, and optoelectronic devices like LEDs. In particular, the ability to prepare CNDs from a wide range of accessible organic materials makes them a potential alternative for conventional organic dyes and semiconductor quantum dots (QDs) in various applications. However, current synthesis methods are typically expensive and depend on complex and time-consuming processes or severe synthesis conditions and toxic chemicals. One way to reduce overall preparation costs is the use of biological waste as starting material. Hence, natural carbon sources such as pomelo peal, egg white and egg yolk, orange juice, and even eggshells, to name a few; have been used for the preparation of CNDs. While the use of waste is desirable, especially to avoid competition with essential food production, most starting-materials lack the essential purity and structural homogeneity to obtain homogeneous carbon dots. Furthermore, most synthesis approaches reported to date require extensive purification steps and have resulted in carbon dots with heterogeneous photoluminescent properties and indefinite composition. For this reason, among others, the relationship between CND structure (e.g. size, edge shape, functional groups and overall composition) and photophysical properties is yet not fully understood. This is particularly true for carbon dots displaying selective luminescence (one of their most intriguing properties), i.e. their PL emission wavelength can be tuned by varying the excitation wavelength.
In this work, a new reliable, economic, and environmentally-friendly one-step synthesis is established to obtain CNDs with well-defined and reproducible photoluminescence (PL) properties via the microwave-assisted hydrothermal treatment of starch, carboxylic acids and Tris-EDTA (TE) buffer as carbon- and nitrogen source, respectively. The presented microwave-assisted hydrothermal precursor carbonization (MW-hPC) is characterized by its cost-efficiency, simplicity, short reaction times, low environmental footprint, and high yields of approx. 80% (w/w). Furthermore, only a single synthesis step is necessary to obtain homogeneous water-soluble CNDs with no need for further purification.
Depending on starting materials and reaction conditions different types of CNDs have been prepared. The as-prepared CNDs exhibit reproducible, highly homogeneous and favourable PL properties with narrow emission bands (approx. 70nm FWHM), are non-blinking, and are ready to use without need for further purification, modification or surface passivation agents. Furthermore, the CNDs are comparatively small (approx. 2.0nm to 2.4nm) with narrow size distributions; are stable over a long period of time (at least one year), either in solution or as a dried solid; and maintain their PL properties when re-dispersed in solution. Depending on CND type, the PL quantum yield (PLQY) can be adjusted from as low as 1% to as high as 90%; one of the highest reported PLQY values (for CNDs) so far.
An essential part of this work was the utilization of a microwave synthesis reactor, allowing various batch sizes and precise control over reaction temperature and -time, pressure, and heating- and cooling rate, while also being safe to operate at elevated reaction conditions (e.g. 230 ±C and 30 bar). The hereby-achieved high sample throughput allowed, for the first time, the thorough investigation of a wide range of synthesis parameters, providing valuable insight into the CND formation. The influence of carbon- and nitrogen source, precursor concentration and -combination, reaction time and -temperature, batch size, and post-synthesis purification steps were carefully investigated regarding their influence on the optical properties of as-synthesized CNDs. In addition, the change in photophysical properties resulting from the conversion of CND solution into solid and back into the solution was investigated. Remarkably, upon freeze-drying the initial brown CND-solution turns into a non-fluorescent white/slightly yellow to brown solid which recovers PL in aqueous solution. Selected CND samples were also subject to EDX, FTIR, NMR, PL lifetime (TCSPC), particle size (TEM), TGA and XRD analysis. Besides structural characterization, the pH- and excitation dependent PL characteristics (i.e. selective luminescence) were examined; giving inside into the origin of photophysical properties and excitation dependent behaviour of CNDs. The obtained results support the notion that for CNDs the nature of the surface states determines the PL properties and that excitation dependent behaviour is caused by the “Giant Red-Edge Excitation Shift” (GREES).
The Cauchy problem for the linearised Einstein equation and the Goursat problem for wave equations
(2017)
In this thesis, we study two initial value problems arising in general relativity. The first is the Cauchy problem for the linearised Einstein equation on general globally hyperbolic spacetimes, with smooth and distributional initial data. We extend well-known results by showing that given a solution to the linearised constraint equations of arbitrary real Sobolev regularity, there is a globally defined solution, which is unique up to addition of gauge solutions. Two solutions are considered equivalent if they differ by a gauge solution. Our main result is that the equivalence class of solutions depends continuously on the corre- sponding equivalence class of initial data. We also solve the linearised constraint equations in certain cases and show that there exist arbitrarily irregular (non-gauge) solutions to the linearised Einstein equation on Minkowski spacetime and Kasner spacetime.
In the second part, we study the Goursat problem (the characteristic Cauchy problem) for wave equations. We specify initial data on a smooth compact Cauchy horizon, which is a lightlike hypersurface. This problem has not been studied much, since it is an initial value problem on a non-globally hyperbolic spacetime. Our main result is that given a smooth function on a non-empty, smooth, compact, totally geodesic and non-degenerate Cauchy horizon and a so called admissible linear wave equation, there exists a unique solution that is defined on the globally hyperbolic region and restricts to the given function on the Cauchy horizon. Moreover, the solution depends continuously on the initial data. A linear wave equation is called admissible if the first order part satisfies a certain condition on the Cauchy horizon, for example if it vanishes. Interestingly, both existence of solution and uniqueness are false for general wave equations, as examples show. If we drop the non-degeneracy assumption, examples show that existence of solution fails even for the simplest wave equation. The proof requires precise energy estimates for the wave equation close to the Cauchy horizon. In case the Ricci curvature vanishes on the Cauchy horizon, we show that the energy estimates are strong enough to prove local existence and uniqueness for a class of non-linear wave equations. Our results apply in particular to the Taub-NUT spacetime and the Misner spacetime. It has recently been shown that compact Cauchy horizons in spacetimes satisfying the null energy condition are necessarily smooth and totally geodesic. Our results therefore apply if the spacetime satisfies the null energy condition and the Cauchy horizon is compact and non-degenerate.
In the arable soil landscape of hummocky ground moraines, an erosion-affected spatial differentiation of soils can be observed. Man-made erosion leads to soil profile modifications along slopes with changed solum thickness and modified properties of soil horizons due to water erosion in combination with tillage operations. Soil erosion creates, thereby, spatial patterns of soil properties (e.g., texture and organic matter content) and differences in crop development. However, little is known about the manner in which water fluxes are affected by soil-crop interactions depending on contrasting properties of differently-developed soil horizons and how water fluxes influence the carbon transport in an eroded landscape. To identify such feedbacks between erosion-induced soil profile modifications and the 1D-water and solute balance, high-precision weighing lysimeters equipped with a wide range of sensor technique were filled with undisturbed soil monoliths that differed in the degree of past soil erosion. Furthermore, lysimeter effluent concentrations were analyzed for dissolved carbon fractions in bi-weekly intervals.
The water balance components measured by high precision lysimeters varied from the most eroded to the less eroded monolith up to 83 % (deep drainage) primarily caused due to varying amounts of precipitation and evapotranspiration for a 3-years period. Here, interactions between crop development and contrasting rainfall interception by above ground biomass could explain differences in water balance components. Concentrations of dissolved carbon in soil water samples were relatively constant in time, suggesting carbon leaching was mainly affected by water fluxes in this observation period. For the lysimeter-based water balance analysis, a filtering scheme was developed considering temporal autocorrelation. The minute-based autocorrelation analysis of mass changes from lysimeter time series revealed characteristic autocorrelation lengths ranging from 23 to 76 minutes. Thereby, temporal autocorrelation provided an optimal approximation of precipitation quantities. However, the high temporal resolution in lysimeter time series is restricted by the lengths of autocorrelation.
Erosion-induced but also gradual changes in soil properties were reflected by dynamics of soil water retention properties in the lysimeter soils. Short-term and long-term hysteretic water retention data suggested seasonal wettability problems of soils increasingly limited rewetting of previously dried pore regions. Differences in water retention were assigned to soil tillage operations and the erosion history at different slope positions. The threedimensional spatial pattern of soil types that result from erosional soil profile modifications were also reflected in differences of crop root development at different landscape positions. Contrasting root densities revealed positive relations of root and aboveground plant characteristics. Differences in the spatially-distributed root growth between different eroded soil types provided indications that root development was affected by the erosion-induced soil evolution processes.
Overall, the current thesis corroborated the hypothesis that erosion-induced soil profile modifications affect the soil water balance, carbon leaching and soil hydraulic properties, but also the crop root system is influenced by erosion-induced spatial patterns of soil properties in the arable hummocky post glacial soil landscape. The results will help to improve model predictions of water and solute movement in arable soils and to understand interactions between soil erosion and carbon pathways regarding sink-or-source terms in landscapes.
The first main goal of this thesis is to develop a concept of approximate differentiability of higher order for subsets of the Euclidean space that allows to characterize higher order rectifiable sets, extending somehow well known facts for functions. We emphasize that for every subset A of the Euclidean space and for every integer k ≥ 2 we introduce the approximate differential of order k of A and we prove it is a Borel map whose domain is a (possibly empty) Borel set. This concept could be helpful to deal with higher order rectifiable sets in applications.
The other goal is to extend to general closed sets a well known theorem of Alberti on the second order rectifiability properties of the boundary of convex bodies. The Alberti theorem provides a stratification of second order rectifiable subsets of the boundary of a convex body based on the dimension of the (convex) normal cone. Considering a suitable generalization of this normal cone for general closed subsets of the Euclidean space and employing some results from the first part we can prove that the same stratification exists for every closed set.